LIVRO DE RESUMOS
Encontro Nacional
ENFE 15 de Física Estatística 1-4 de Novembro de 2015 Vitória-ES
COMITÊ NACIONAL Roberto Andrade (UFBA) Ronald Dickman (UFMG) Dora Izzo (UFRJ) Tarcísio Marciano (UnB) João Plascak (UFPB) Carmen Prado (USP) Silvio Salinas (USP) José Soares Andrade Jr. (UFC) Constantino Tsallis (CBPF)
COMITÊ ORGANIZADOR Celia Anteneodo (PUC-Rio) Jeferson Arenzon (UFRGS) Marcia Barbosa (UFRGS) Marcos G. E. da Luz (UFPR) Gandhi Viswanathan (UFRN)
Local do evento: Sheraton Vitoria Hotel, Av. Saturnino de Brito 217, Praia do Canto, Vitória, ES Mais informações: http://enfe.fis.puc-rio.br Contato: [email protected]
UFES-CCE
1 Plenary talks (8:30 - 10:00) Posters (10:00-11:00 / 16:05-17:05)
PLENARY SESSION COMPLEXITY & INTERDISCIPLI- NARY TOPICS [02/11/2015 - 09:00 - Room Vit´oria] A random walk picture of basketball scoring and [02/11/2015 - P001] lead-change dynamics, Aaron Clauset, Marina Spatial organization and mobility effects in collec- tive hunting and defense strategies of predator- Kogan, Sid Redner, Santa Fe Institute By analy- ´ zing recently available play-by-play data from all regular- prey systems, Annette Cazaubiel, Ecole Normale season games from multiple seasons of the National Bas- Sup´erieure - International Center of Fundamental Phy- ketball Association (NBA), we present evidence that, sics, Paris - France, Alessandra F. Lutz¨ , Jeferson basketball scoring during a game is well described by a J. Arenzon, Instituto de F´ısica - UFRGS , Porto Ale- continuous-time anti-persistent random walk. The time gre RS - Brasil There is a myriad of strategies that intervals between successive scoring events follow an ex- predators utilize to increase their rate of success. Among ponential distribution, with essentially no correlations them, preys may be attacked in a cooperative, coordina- between different scoring intervals. We will also argue ted way, these actions being correlated in space and time. that the heterogeneity of team strengths plays a minor The number of known examples of coordinated hunting, role in understanding the statistical properties of basket- whether intra or interspecies, has increased in the last ye- ball scoring. ars and examples include hawks, crocodiles, spiders, etc. As intriguing applications of this random-walk picture, Although there are some additional costs, hunting or de- we show that: (i) the distribution of times when the last fending in group may bring several benefits for predators lead change occurs, (ii) the distribution of times when and preys, respectively, what have been widely studied. the score difference is maximal, and (iii) the distribution Despite these mounting evidences, much less attention for the fraction of game time that one team is leading are has been dedicated to model such behavior. all given by the celebrated arcsine law–a beautiful and This problem has been recently considered within a game surprising property of random walks. We also use the theoretical framework in which the abundances of preys random-walk picture to construct the criterion for when and predators were assumed constant and only the frac- a lead of a specified size is ”safe”as a function of the time tion of those populations using either an individual or remaining in the game. This prediction generally agrees collective strategy evolves. Lett et al (2004 Theor. Pop. with comprehensive data on more than 1.25 million sco- Biol. 65 263) considered a mean field approach in which ring events in roughly 40,000 games across four profes- these densities are described by Lotka-Volterra-like equa- sional or semiprofessional team sports, and are more ac- tions, taking into account some of the advantages and curate than popular heuristics that are currently used in disadvantages for both preys and predators choosing a sports analytics. grouping strategy. More specifically, it is assumed that grouping lowers the risk of predation at the cost of incre- [02/11/2015 - 09:30 - Room Vit´oria] asing the competition for resources, while predators have CLUSTER APPROACH TO GELS AND a greater probability of success at the expense of having GLASSES, A. Coniglio, CNR-SPIN, Department of to share the prey with others. Physics, University of Naples “Federico II”, Via Cinthia, We present a spatial version of this model that locates 80126 Napoli, Italy A percolation theory is presented individuals or groups on a lattice and study it in the li- to describe the dynamics of the sol-gel transition[1]. mits of both low and high population viscosity (with or The same approach at mean field level is shown to without diffusion, respectively), and compare these re- describe also the dynamical critical behavior predicted sults with the mean field predictions. Of particular inte- by mode coupling theory (MCT) for the continuous glass rest is the coexistence region with both grouped and indi- transition[2]. A similar approach is extended to MCT vidual predators and prey persist within the population. for the discontinuous glass transition, more appropriate When compared with the mean field case, fundamental to describe the standard molecular glass transition. It is differences appear and are strongly affected by finite size shown that the relevant model now is given by Bootstrap effects. Percolation. This approach will provide a geometrical and physical interpretation of the critical exponents, [02/11/2015 - P002] Density classification performance of the elucidating the scaling laws and the universal aspect of Gacs-Kurdyumov-Levin four-states cellular MCT. automaton model IV and related automata, J. Ricardo G. Mendonc¸a, Rolf E. O. Simoes,˜ [1] A. Fierro, T. Abete and A. Coniglio, J. Chem. Phys. EACH/USP Almost four decades ago (in 1978), Gacs, 131, (2009) 194906. Kurdyumov, and Levin (GKL) introduced three different [2] J..J. Arenzon, A. Coniglio A. Fierro, and M. Sellitto. cellular automata (CA), which they called models II, Phys. Rev. 90, (2014) 020301(R) IV, and VI, to investigate whether nonequilibrium interacting particle systems are capable of displaying phase transitions. Their objective was to examine the “positive probabilities conjecture,” according to which one-dimensional particle systems with short-range inte- ractions and positive transition probabilities are always ergodic. This conjecture has been disproved—much 2 Abstracts - ENFE - 02/11/2015 to the awe of the practicing community—many times is to make a change of variable t for a new log-time since then, with the introduction of several models that τ ln(tc t), then to study the power spectrum of the have become archetypal models in theoretical computer new≡ series− thus generated. A consequence of this method science and nonequilibrium statistical mechanics. is the non-uniformity of the sample data, i.e. unequal spa- As a by-product of their investigations, GKL introduced cing between data points. The FFT-based techniques are the density classification problem in the cellular auto- not applicable, but one solution is to use the Lomb perio- mata literature. The density classification task consists dogram of Scargle, which is suitable for unevenly sampled in classifying arrays of symbols according to their ini- points. tial density of symbols using local rules, and is comple- We applying this method to study the Brazilian finan- ted successfully if a correct verdict as to which was the cial market, with the aim of detecting discrete scale inva- initial majority state is obtained in time at most linear riance in the Bovespa (Bolsa de Valores de S˜ao Paulo) in the size of the input array. Density classification is stock market index. Some historical price series have a nontrivial task for CA in which cells interact over fi- been selected for the periods in 1999, 2001 and 2008. We nite neighbourhoods, because then the cells have to achi- report evidence of detection of possible log-periodicity eve a global consensus cooperating locally only. Ultima- before breaks. tely, that means that information should flow through [02/11/2015 - P004] the entire system, be processed by the cells, and be not Study of String-Like Excitations in Artificial Spin destroyed or become incoherent in the process—entropy Ice Through Linear Chains of Magnetic Dipoles, must loose to work in the task, a relevant property in the Denis da Mata Oliveira, Lucas Alvares da Silva theoretical analysis of data processing and storage under Mol,´ UFMG In this work we study a system of classi- noise. For one-dimensional locally interacting systems of cal magnetic Ising-like dipoles (spins) on the square lat- autonomous and memoryless cells, emergence of collec- tice interacting exclusively by magnetic dipolar interac- tive behavior is required in these cases. In this context, tion. The spins are positioned in sequence, forming linear GKL model II has been extensively scrutinized as a model chains on the lattices links (strings), parallel to its plane. system related with the concepts of emergence, communi- These strings are constructed by Self-Avoiding Walks cation, efficiency, and connectivity. The other two GKL (SAW’s). For each string length, we generate all reacha- models, however, did not receive much attention. ble microstate the system in order to make the accurate Here we characterize the density classification perfor- analysis of the system through the canonical ensemble. mance of Gacs, Kurdyumov, and Levin’s “model IV,” a Our purpose is to better understand the behavior of ex- four-states cellular automaton with three absorbing sta- citation type strings in artificial spin ice, since the studied tes, by Monte Carlo simulations. We show that model IV chains are similar to those excitations, which present as compares well with its sibling model II in the density clas- remarkable feature the presence of magnetic monopole sification task, the additional states being barely relevant quasi-particles associated to its extremes. The studied for its performance. We also investigate the performance system is similar to the homopolymers in network-based of model IV under the influence of noise and show that SAW’s. We observed signs of phase transition which are it cannot perform the density classification task reliably analyzed by such quantities as the end-to-end distance at any nonzero level of noise, an indication that, most and the radius of gyration. Among the phase transi- probably, it becomes ergodic in this case. tion signs observed, the compact-extended transition of strings is well identified, such as the θ-transition of ho- [02/11/2015 - P003] Discrete Scale Invariance in Self-Organized Criti- mopolymers. We also present some results for the he- cality Systems, Andre´ Luis Brito Querino, Uni- xagonal lattice. We observed that the low temperature properties of the square lattice are determined by confi- versidade de S˜ao Paulo USP Recently, studies have shown evidence of log-periodic behavior in non- gurations that satisfy a rule of alternation in the direction hierarchical systems. A known case of log-periodicity of the walk, while in the hexagonal lattice the minimum or discrete scale invariance are systems that have a ge- end-to-end distance is the key factor. ometric hierarchy, for example the model Potts on the Thanks financial support: CNPq e FAPEMIG. diamond structure. The usual solutions of the renorma- [02/11/2015 - P005] lization group show that such systems have power laws Role of dimensionality of complex networks with 1 xb with complex exponents b C when near a critical metrics: Connection with nonextensive statistical point. An interesting fact is the∈ emergence of such pro- mechanics, S.G.A. Brito, L.R. da Silva, Depar- perties in real systems, for instance rupture and break- tamento de F´ısica Te´orica e Experimental - UFRN, C. down of complex materials and financial crashes. These Tsallis, Centro Brasileiro de Pesquisas F´ısicas - CBPF may be examples of complex systems with self-organized and Santa Fe Institute The study of networks is per- criticality (SOC). ceived in several fields of the science since many real sys- The detection of discrete scale invariance, or log- tems can be modeled as networks. The networks are periodicity in non-hierarchical systems presents nume- everywhere from social science to physics, biology, eco- rous difficulties. Parametric estimates using log-periodic nomics and other areas. Over the last decade a large functions can be flawed due to large fluctuations in va- number of empirical studies has been identifying pecu- lues, beyond the problem of degeneracy and multiple lo- liar properties in very different networks, for instance, cal minima in parametric regression estimation. For these the Internet and Online Social Networks (e.g. Facebook) reasons most research focuses on the use of nonparame- to citation networks and networks of neurons. Over the tric methods in detecting discrete scale invariance. A past years the concept of nonextensive statistical mecha- method widely used for the study of log-periodic data nics has been extremely successful in applications of the ENFE - 02/11/2015 - Abstracts 3 complex systems, in particular, on the complex networks. spatial scenarios in models under certain special condi- Deep connections are known to exist between scale-free tions. We follow another route, where the social inte- networks and non-Gibbsian statistics. For example, the ractions between any two agents is given by the descent typical degree distributions at the thermodynamical limit along the gradient of a cost function deduced from a Baye- k/κ are of the form P (k) eq− , where the q-exponential sian learning formalism. The cost functions depends on z ∝ 1 a hyperparameter that estimates the trust of one agent form e [1 + (1 q)z] 1 q optimizes the nonadditive q ≡ − − on the information provided by the other. If the expec- entropy Sq, basis of nonextensive statistical mechanics (which recovers Boltzmann-Gibbs statistical mechanics ted value of the total cost function is relevant informa- at the q 1 limit). We introduce and study here d- tion, Maximum Entropy permits characterizing the state dimensional→ growing networks with preferential attach- of the society. Furthermore we introduce a dynamics on αA the trust parameters, which increases when agents concur ment involving Euclidean distances through r− (αA ij ≥ and decreases otherwise. We study the resulting phase di- 0). Reinforcing the connection with q-statistics we nume- agram in the case of large number of interacting agents rically verify that the q-exponential degree distributions on a complete social graph, hence under sympatric con- exhibit, for both q and κ, universal dependences on the ditions. Simulations show that there is evolution of as- ratio α /d. Moreover, the q = 1 limit is exponentially A sortative distrust in rich cultural environments measured achieved by increasing α /d to infinity. A by the diversity of the set of issues under discussions. [02/11/2015 - P006] High distrust leads to antilearning which leads to mul- Contribution to the study of complex networks: tiple groups which hold different opinions on the set of Affinity model with metrics, S.G.A. Brito, L.R. issues. We simulate conditions of political pressure and da Silva, Departamento de F´ısica Te´orica e Experimen- interaction that describe the House of Congress of Bra- tal - UFRN Currently the interest in large-scale sys- zil and are able to qualitatively replicate voting patterns tems with a high degree of complexity has been much dis- through four presidential cycles during the years of 1994 cussed in the scientific community in various areas of kno- to 2010. wledge. As an example, the Internet, protein interaction, collaboration of film actors, among others. To better un- [02/11/2015 - P008] Spectral analysis of complex network with tuna- derstand the behavior of interconnected systems, several ble degree distribution and clustering, Roberta models in the area of complex networks have been propo- Pires Lins Machado, Josue´ Xavier de Carvalho, sed. Barab´asi and Albert proposed a model in which the Universidade Federal do Rio de Janeiro - Campus Xer´em connection between the constituents of the system could Network models provide a natural way to describe real dynamically and which favors older sites, reproducing a data set in diverse fields as for example biology, sociology, characteristic behavior in some real systems: connecti- ecology, internet, global economy and many others. Real vity distribution of scale invariant. However, this model networks display topological features, such as heavy tail neglects two factors, among others, observed in real sys- degree distribution, high clustering coefficient and assor- tems: homophily and metrics. Given the importance of tativity or disassortativity, that can not be modeled by a these two terms in the global behavior of networks, we totally regular or random graphs. Many random network propose in this dissertation study a dynamic model of pre- models has been proposed with the aim to capture featu- ferential binding to three essential factors that are respon- res regularly found in empirical networks. Two of most sible for competition for links: (i) connectivity (the more studied classes of such models are the Scale-free network connected sites are privileged in the choice of links) (ii) model (SF) and the Small-world network model (SW). homophily (similar connections between sites are more The original SF model display power law degree distri- attractive), (iii) metric (the link is favored by the proxi- bution and vanishing clustering coefficient in the limit mity of the sites). Within this proposal, we analyze the of large networks. The SW model interpolates between behavior of the distribution of connectivity and dynamic regular and random network by means a parameter p, evolution of the network are affected by the metric by that characterizes the disorder in the system. For small α parameter that controls the importance of distance A values of p the model exhibits high clustering coefficient. in the preferential binding) and homophily by η (cha- Since each graph/network can be represented by a matrix racteristic intrinsic site). We realized that the increased (adjacency, laplacian or normalized laplacian) its spectra importance as the distance in the preferred connection, (eigenvalues and eigenvectors) encodes information about the connections between sites and become local connec- its topology. The fluctuations of networks spectra can tivity distribution is characterized by a typical range. In be analysed through the framework of Random Matrices parallel, we adjust the curves of connectivity distribution, k/ηq Theory (RMT). Results for SW model have revealed that for different values of αA, the equation P (k)= P0e−q as the disorder level increases (decreasing clustering co- from the statistical non-extensive Tsallis. efficient) the spectral fluctuations follows the description [02/11/2015 - P007] of a transition between two different ensemble of RMT Sympatric multiculturalism or how distrust po- (Poisson-GOE transition). The main focus of this work larizes societies of Bayesian agents into groups, is to clarify the effects of clustering on the spectral pro- Felippe Alves, Nestor Caticha, IF Universidade de perties of complex networks. The clustering quantifies S˜ao Paulo While social interactions tend to decrease the likelihood that two neighbors of a vertex are neigh- differences in opinions, multiplicity of groups and indivi- bors themselves and it is related to number of triangles in dual opinion differences persist in human societies. Axel- the network (the vast majority of real networks display a rod identified homophily and social conformity seeking high density of triangles). The spectra of totally random as basic interactions that can lead to multiculturalism in networks (no correlation between vertices) is well descri- 4 Abstracts - ENFE - 02/11/2015 bed by GOE ensemble of RMT. According to RMT it is lit`ecnica de Catalunya The heterogeneous topology of expected that network models with high clustering (cor- a complex network can have a very relevant impact on the relation) deviates from GOE prediction. Here we analyse properties of dynamical systems running on top of it. Al- under the RMT framework the spectral properties of dif- ready classical studies in network science have thus shown ferent classes of random networks where both the degree- that a heterogeneous connectivity pattern can lead to a dependent clustering coefficient and the degree distribu- null percolation threshold, set a strong resilience against tion are tunable with special attention to the Scale-free random failures, as well as to induce a vanishing epide- networks. mic threshold for disease propagation. Similar and ad- [02/11/2015 - P009] ditional remarkable effects have been observed in a wide A resource based model for the competition of two variety of dynamical processes. Such dynamical effects, species with different metabolic pathways, Andre´ originally reported for static networks, in which nodes Amado†, Jorge Lenin†, Weini Huang‡, Paulo R. and edges are fixed and do not change over time, can A. Campos†, Fernando F. Ferreira§, †Evolutionary take a different, more complex turn when one considers Dynamics Lab, Department of Physics, Federal Univer- the intrinsic time-varying, temporal nature of many real sity of Pernambuco, 50670-901, Recife-PE, Brazil networks. Indeed, networked systems are often not static, ‡Department Evolutionary Theory, Max Planck Institute but show connections which appear and disappear with for Evolutio The evolution of cooperation is one of some characteristic time scales. Social networks represent the most intriguing conundrum in evolutionary biology. the prototypical example of this behavior, being defined Natural selection favours traits that increase individuals in terms of a sequence of social contacts that are continu- ability to reproduce or survive. One individual is said to ously established and broken. This mixing of time scales be cooperative if it provides a benefit to another indivi- can induce new phenomenology on dynamics on temporal dual or to a group at the expense of its own relative fit- networks, in stark contrast with what is observed in static ness. According to evolutionary theory, such cooperative networks. Moreover, the bursty nature of the time evolu- behaviour is detrimental to the individual and should be tion of temporal network contacts, characterized by long counter-selected. Instead, the selfish behaviour is expec- stretches of inactivity, interspersed by bursts of intense ted to rise and invade in a group of cooperators. However, activity, can complicate the picture, inducing for example cooperation is observed everywhere. Despite the greater a dynamical slowing down in dynamical processes as va- attention the issue has received in the last decades our ried as epidemic spreading, diffusion or synchronization. understanding about the underlying mechanisms that ex- The random walk is one of the simplest dynamical pro- plain the emergence and maintenance of cooperation is cesses, although still underlying many practical realistic still poor. Here we combine the frameworks of resource- applications such as diffusion, searching, community de- based modeling and evolutionary game theory to study tection and spreading dynamics. Even in this simplest of the conditions under which cooperative strains can thrive cases, a time-varying substrate can induce very noticea- in the context of metabolic pathways. ble differences with respect to the behavior expected in Heterotrophic organisms can produce adenosine static networks. In this work, we investigate the dynamic triphosphate (ATP) from two different mechanisms: relaxation of random walks on temporal networks by fo- inefficient (high rate) in which high amount of resources cusing in the recently proposed activity driven model [N. is consumed or efficient (high yield) with less resource Perra, et. al. Sci.Rep. 2, 469 (2012)]. For realistic acti- consumption. Despite cells with a higher rate but lower vity distributions with a power-law form, we observe the yield of ATP production may have a selective advantage presence of a very slow relaxation dynamics compatible compared with high yield cells, the latter is abundant with aging effects. A theoretical description of this pro- in nature. To be well succeeded the high yield cells cesses in achieved by means of a mapping to Bouchauds behave as a cooperative organism while high rate cells trap model. The mapping highlights the profound diffe- are non-cooperative. This problem can be posed in terms rence in the dynamics of the random walks according to of competition between cooperative and selfish cells. the value of the exponent γ in the activity distribution. Here we investigate the probability that a cooperative Acknowledgements and Financial Support: FAPEMIG, trait can invade a population of defectors (high rate of CAPES and CNPq. consumption, but low yield of conversion of research into [02/11/2015 - P011] energy) by using multilevel selection, where individuals Nonequilibrium phase transitions in a model of (cells) are organised into groups. Selection occurs at tax evasion dynamics, Rafael Mynssem Brum, both individual and group levels. Selection at the group Nuno Crokidakis, Instituto de F´ısica, Universidade level stems from differentiated growth rates that vary Federal Fluminense, Niter´oi/RJ, Brazil The agent- according to the group’s composition. We show in what based modeling of social interactions is one of the most conditions high yield cells can invade a population of interesting problems in statistical physics and it has been high rate metabolic cells. One of the motivation to extensively explored due to its high degree of applicability study this problem is understanding the transition of (opinion dynamics, spreading of diseases, systems with unicellular organism (high rate) to multicellular (high competing dynamics, rumor spreading, etc). Its results yield). are also very important from the point of view of an orga- [02/11/2015 - P010] nized society (stationary behavior of a disease, epidemic Slow relaxation dynamics and aging in ran- cycles, predominance of a certain political position and dom walks on activity driven temporal networks, many others). Angelica´ Sousa da Mata, Universidade Federal de In this work, we study the tax evasion dynamics in a Lavras, Romualdo Pastor-Satorras, Universitat Po- artificial society. In this case, we consider three types ENFE - 02/11/2015 - Abstracts 5 of individuals in relation to tax compliance: honest, tax change. In complex systems bifurcations can be associ- evaders and undecided individuals. We analyze the social ated with phase transitions in many different contexts: interactions that may occur among these individuals and from ecosystems to models of information traffic on the autonomous decisions, and we consider our population Internet, and from epidemic to social models. as a fully-connected network of N nodes, that characte- But if a complex system undergoes a phase transition rize a mean-field-like approach. Through analytical and when the control parameter reaches some critical value, numerical results, we found that even if initially there which are the critical aspects (in the sense of thermodyna- are no tax evaders in the population, these individuals mics / statistical mechanics) of such a transition? Trying may emerge in the society, and its fraction may stabilize to answer this question, it is presented an exploratory in the population, depending on certain socio-economic study, based on Thermodynamic Geometry (TG), of the parameters (efficiency of the influence of certain individu- critical aspects of some common bifurcations (e. g. trans- als over others, autonomous decisions, punishment rules, critical, saddle-node, etc.). etc). We show that this emergency of tax evaders is as- Thermodynamic Geometry (TG), also called Information sociated with a nonequilibrium phase transition. Geometry, is an approach based on Riemannian geome- try for the study of thermodynamical systems in equili- COMPLEXITY & INTERDISCIPLI- brium. The main idea is that the space of equilibrium NARY TOPICS states of a system is described by a metric, which is pro- portional to the Hessian matrix of entropy (or another [02/11/2015 - P012] thermodynamic potential) of the system with respect to On a connection between a class of q-deformed al- the thermodynamic parameters. In this context, the no- gebras and the Hausdorff derivative in a medium tion of “distance” between two states is associated with with fractal metric, Jose´ Weberszpil, Universidade probability of fluctuation between them: the less likely Federal Rural do Rio de Janeiro, UFRRJ-IM/DTL, Av. the fluctuation between the states, more distant they are. Governador Roberto Silveira s/n, Nova Igua¸c´u, Rio de From the metric one can obtain the corresponding geo- Janeiro, RJ, Brazil, Matheus Jatkoske Lazo, Uni- desic equations and curvature scalar R, which in turn is d versidade Federal do Rio Grande-FURG, Instituto de Es- proportional to the correlation volume ξ and therefore tat´ıstica e F´ısica, Rio Grande, RS, Brazil, Jose´ Ab- closely related to phase transitions. dalla Helayel-Neto,¨ Centro Brasileiro de Pesquisas In order to study the critical aspects of bifurcations in F´ısicas-CBPF-Rua Dr Xavier Sigaud 150, 2290-180, Rio such a geometrical approach, the normal form (described de Janeiro, RJ, Brazil Over the recent decades, di- by a nonlinear first-order differential equation) of each bi- verse formalisms have emerged that are adopted to ap- furcation is regarded (after some appropriate transforma- proach complex systems. Amongst those, we may quote tions) as a geodesic equation of some hypothetical model. the q-calculus in Tsallis version of Non-Extensive Sta- With this we obtain the corresponding metric, curvature tistics with its undeniable success whenever applied to scalar and also the exponent α, analogous to the critical a wide class of different systems; Kaniadakis approach, exponent of specific heat in a typical thermodynamical based on the compatibility between relativity and ther- system. modynamics; Fractional Calculus (FC), that deals with [02/11/2015 - P014] the dynamics of anomalous transport and other natural Mean-field approximation for the Sznajd model phenomena, and also some local versions of FC that claim in complex networks, Maycon S. Araujo,´ Andre´ to be able to study fractal and multifractal spaces and to M. Timpanaro, Carmen P. C. do Prado, USP - SP describe dynamics in these spaces by means of fractio- - Brazil, Fabio´ S. Vannucchi, UNESP - SP - Brazil nal differential equations. The question we might ask We will present a work in which we revisited mean fied is whether or not there are common aspects that con- approximations to the Sznajd model for opinion forma- nect these alternative approaches. In this short com- tion in a population connected through a general network. munication, we discuss a possible relationship between A master equation describing the time evolution of opi- q-deformed algebras in two different contexts of Statisti- nions is presented and solved in a hybrid approach. Ba- cal Mechanics, namely, Tsallis framework and Kaniadakis sed in a mean-field approximation, we were able to in- scenario, with local form of fractional derivative operators clude some features of the underling structure of the defined in fractal media, the so-called Hausdorff deriva- network though the estimate of some network parame- tives, mapped into a continuous medium with a fractal ters. Although quite simple, this approximation allows us measure. This connection opens up new perspectives for to capture the most important features regarding the ste- theories that satisfactorily describe the dynamics for the ady states of the model. When spontaneous opinion chan- transport in media with fractal metrics, such as porous ges are included, a discontinuous transition from consen- or granular media. Possible connections with other alter- sus to polarization can be found as the rate of sponta- native definitions of FC are also contemplated. Insights neous change is increased. The main point in this work on complexity connected to concepts like coarse-grained is the presentation of a hybrid mean-field approach, that space-time and physics in general are pointed out. includes interactions between second nearest neighbors, [02/11/2015 - P013] that are necessary to estimate correctly the critical point Critical aspects of bifurcations in a geometrical of the transition. The analytical prediction of the cri- approach, A. Mihara, Universidade Federal de S. tical point is also compared with numerical simulations Paulo Bifurcation is a qualitative change that occurs in a wide variety of networks, in particular Barab´asi- in the behavior of a dynamic system when the value Albert networks, finding reasonable agreement despite of a (control) parameter undergoes a small and smooth the strong approximations involved. The same hybrid 6 Abstracts - ENFE - 02/11/2015 approach that made it possible to deal with second-order tions, several quantities characterizing the mixed-games neighbors could just as well be adapted to treat other pro- are still the same as the ones obtained in the average blems such as epidemic spreading or predator-prey sys- game when the two games are not very different. Also we tems. The work has been published in PRE 91, 022813 find interesting results regarding how the heterogeneity (2015). of the games played can increase the final fraction of coo- perators above the usual mean game limit. We would like [02/11/2015 - P015] Interspike intervals in neuronal networks with to thanks FAPEMIG and CNPq for the financial support self-organized criticality, Osame Kinouchi, Ari- given. adne A. Costa, Lezio´ Bueno, Geraldine Bosco, [02/11/2015 - P017] Universidade de S˜ao Paulo, Mauro Copelli, Universi- Differences between quenched and annealed dade Federal do Pernambuco The distribution of inters- neuronal networks with self-organized critica- pike intervals (ISI) for individual neurons is a standard lity, Ariadne de Andrade Costa, Osame Kinou- measure in neuroscience. Recently the idea that neuro- chi, FFCLRP - USP - SP - Brasil, Joao˜ G. F. Cam- nal networks works near the critical point of an absorbing pos, Mauro Copelli, UFPE - PE - Brasil In a re- state transition has been explored, with a lot of theoreti- cent work, mean field analysis and computer simulations cal and experimental results. Surprisingly, it appears that were employed to analyze critical self-organization in an the distribution of ISI for neurons pertaining to a criti- annealed network of excitable cellular automata (SIRS) cal network has not been measured yet. Here, we model neuronal networks, where randomly chosen synapses are the generation of interspike intervals in neuronal systems depressed after each neuron spike. Calculations agree with self-organized criticality by two methods. First, we with simulations of the annealed version, showing that use a simple stochastic model where interavalanches in- the nominal branching ratio (σ) converges to the critical tervals (IAI) are generated from a power law distribution, value σc = 1 and fluctuations vanish in the thermodyna- and interspike intervals are sums of IAI between two times mic limit, as expected of a self-organized critical system. where a neuron spikes because it pertains to an avalan- However, the question remains whether the same results che (modeled by a neuronal size avalanche distribution occurs to the quenched version of the model (which is bi- 3/2 P (S)= cS− ). Second, we perform a full simulation in ologically more plausible) where neighborhoods are fixed a network of excitable elements (neurons) with dynamical and only the acting synapses are depressed. We have seen synapses which presents well behaved self-organized criti- that simulations of the quenched model yield a stationary cality. In this simulation we define avalanches as sequen- value σ(t )=1.105 which is a significant deviation tial activity above some threshold level of active sites. from σ =→ 1, ∞ due to spatio-temporal correlations produ- This enables us to define interavalanches (IAI) and inters- ced by avalanches. However, the model is shown to be pikes intervals (ISI) and construct histograms for them. critical, as the largest eigenvalue λ of the synaptic matrix We compare these results with ISI distributions that pre- is shown to approach λc = 1, with fluctuations vanishing sent power law tails from real neurons from cortical and in the thermodynamic limit. We also study the influence thalamic areas of freely behaving rats. We find that self- of the recovery and decay synaptic parameters in both organized criticality can explain power laws in the tail of types of models, as well the influence of the number of ISI distributions of neurons and that such power laws in neighbors. As a future work, we intend to study the dis- single neurons could suggest the presence of criticality at tribution of interspike intervals in this kind of neuronal the network level. networks. [02/11/2015 - P016] [02/11/2015 - P018] Cooperation in two-dimensional mixed-games, Real genomic representation for topopatric speci- Marco Antonio Amaral, Jafferson Kamphorst ation, Camilo Rodrigues Neto, Sergio Candido Leal da Silva, Lucas Wardill, Universidade Fe- de Oliveira Junior, EACH, University of Sao Paulo, deral de Minas Gerais - MG - Brasil, University of Brasil The evolutionary theory for speciation has pro- British Columbia - Vancouver Vancouver, BC, Canada duced several models to explain the diversity of life. Four Evolutionary game theory is a common mathematical of these models are called alopatric, peripatric, parapa- framework to study the evolution of cooperation in sel- tric and sympatric, named after the predominant kind fish systems, specially using the Prisoners Dilemma game, of genetic flux disturbance acting among the population. where it is usually assumed that the same game is played Physical barriers and ecological interactions are the two in all interactions. Here, we investigate a model where usual factors. the game that is played by two individuals is uniformly Recently, a new kind of speciation was proposed [Aguiar, drawn from a sample of two different games at each itera- 2009]. The model is based in selective mating determined tion. Using the master equation approach we show that by genetic affinity and spatial proximity. The model does the random mixture of two games is equivalent to play not include any kind of geographical barrier, ecological the average game when (i) the strategies are statistically interaction or natural selection. This new kind of specia- independent of the game distribution and (ii) the transi- tion is named topopatric, as it emphasize the role of the tion rates are linear functions of the payoffs. This result spatial auto organization of the species origin and distri- still holds using Pair-Approximation for a small cluster of bution. The usual approach is to represent a specimen as 8 sites arranged in a square lattice. We also use Monte- a binary string, and defying usual genetic algorithm with Carlo simulations in a two dimensional lattice to investi- crossover and mutation operators, but without the se- gate the scenario when the two above conditions do not lection phase. Differences between individuals reproduc- hold, i.e. we use the Fermi-Dirac distribution for the tive rates are randomly attributed at reproduction time, transition rates. We find that even outside of such condi- rather than being due to any special ability. ENFE - 02/11/2015 - Abstracts 7
We present a modified model with a real-coded genetic N, residual correlations will eventually drive it to ther- algorithm, where the specimens are represented by real modynamic equilibrium (if such equilibrium exists, which numbers, with modified crossover and mutation opera- is not the case for 3d gravitational systems) after a time tors. The reproductive rates are similar to the previous t which scales with N as t N δ, where δ is a system binary model. We studied the number of new species, specific× exponent. On the other× ∼ hand, in the thermody- the abundance of the species, and the distribution of the namic limit, N , the system will remain trapped in species over space in function of the genomic distance to- a stationary state→ forever.∞ In this collisionless limit, the lerance, the searchable radius for mating, the migration relaxation to stationarity is a result of Landau damping, and the random reproductive rate. All simulations start which transfers the energy of collective oscillations to the with an initially uniform population, with the same real individual particles. Once the oscillations of the mean- coded genetic algorithm crossover and mutation opera- field potential die out, the particles will move in a static tors, and were performed in torus and ring like spatial mean-field potential. If a system has sufficient symmetry, setups. The results resemble the ones already reported the motion of particles in a static potential will be inte- in the literature, but are not strictly equivalent. We at- grable, and the ergodicity will be irrevocably broken. In tribute this difference mainly to topological differences in this paper we will explore the role of chaotic dynamics on the space of the genome representation. the time that a system with LR interactions remains trap- Aguiar, M. A. M., et al. ”Global patterns of speciation ped in a QSS. We discover that a small degree of chaos, and diversity.”Nature 460.7253 (2009): 384-387. measured by the Lyapunov exponents, favors a faster re- laxation to equilibrium. Surprisingly, a larger degree of [02/11/2015 - P019] Long-range correlations of the wind velocity chaos hinders the relaxation to equilibrium. in Salvador-BA, Jose´ Vicente Cardoso Santos, [02/11/2015 - P021] Davidson Martins Moreira, Marcelo A. Moret, Entropic simulations of the spin-1/2 Baxter-Wu SENAI CIMATEC The use of wind energy has been model., Lucas Nunes Jorge, Alvaro´ de Al- increasingly adopted worldwide. In Brazil, the Northeast meida Caparica, Universidade Federal de Goi´as - UFG has been a strong investment option in the industry be- Among the various models used to describe spins sys- cause recent wind maps have been made and show high tems the Baxter-Wu model is particularly interesting, attendance rates winds around its coastline and in some since it considers triplets of spins, thus, it does not pre- cases inside. Notwithstanding this great wind potential sents spin-reversal symmetry, as it occurs in the most scenario, Brazil has this alternative source of energy with know models. This model is defined in a triangular two- a low representation in its energy mix. Thus, in order dimensional lattice, and the three-spin interaction is gi- to justify an increase in interest and reliability in this ven by the Hamiltonian, alternative source of energy, is presented in this paper a preliminary analysis of time series representing the in- H = J s s s , (1) BW − i j k tensity records and wind direction in fixed unit of data
shrimp shape rotated around a focal point, called perio- [02/11/2015 - P044] dicity hubs, with intricate connections between different Exploiting the weakness of preferential attach- shrimps. ment networks, Tiago M. Vieira, Gandhi M. The purpose of this work is to further develop our recent Viswanathan, Luciano R. da Silva, UFRN - RN - study and we focus on periodicity hubs. Such hubs shows Brasil We address the general problem of how to at- focal points where your localization are associated with tack and destroy a network by node removal given limi- the generation recombination rate. In the present model ted or no prior information about the edges. Networks the coefficients of g-r processes, like as impact ioniza- have been used to describe many kinds of systems. In tion and field enhanced trapping, depend on the electric general, nodes represent systems components and edges field. Our results shows the impact when a small variati- the interactions between them. How the edges are arran- ons on some parameter of the coefficients g-r can causes ged in a network has great importance because quantities on position of the focal points and consequently over all of interest depend on edge placement, e.g. connectivity self-organized periodic structure around them. Our re- distribution, clustering coefficient, resilence to node and sults show that the position of the focal points and the edge removal, spreading processes, and small-world ef- structures of the periodic hubs have dependence with the fects. The rules controlling edge placement define the change of the coefficients g-r. The stable and unstable network structure and they can be exploited by agents hubs and many mergers between shrimps with different that wish to attack weaknesses of the networks. In our periodicity are presented. study, we consider a family of strategies in which nodes [1] da Silva, S. L., Viana, E. R., de Oliveira, A. G., Ri- are randomly chosen, but not removed. Instead a ran- beiro, G. M. and da Silva, R. L. - Int. J. Bifurcation dom acquaintance (i.e., a first neighbour) of the chosen Chaos 25, 1530004 (2015). node is removed from the network. Our approach is a ge- [2] Viana, E. R., Rubinger, R. M., Albuquerque, H. A., neralization of the strategy introduced by Cohen et. al. Dias, F. O., de Oliveira, A. G. and Ribeiro., G. M. - [Phys. Rev. Lett., 91 (2003)], in which the acquaintance Nonlinear Dyn. 67, 385-392 (2012). of a randomly chosen node is promptly removed from the network as soon as it was chosen. Instead of the imme- diate removal, a given node needs to be pointed by other [02/11/2015 - P046] Dynamical Properties of Soft Elliptical Billiard, randomly chosen nodes more than once before being re- Tiago Kroetz, Universidade Tecnol´ogica Federal do moved. As a result, we observe that our approach leads Paran´a, Pato Branco - PR - Brasil, Hercules Alves the network to be destroyed more quickly, i.e., it’s neces- de Oliveira Junior, Universidade Tecnol´ogica Fede- sary to remove a lower number of nodes, in comparison ral do Paran´a, Ponta Grossa - PR - Brasil Two- to the original strategy. dimensional billiards can be considered as special cases [02/11/2015 - P045] of two-dimensional potentials. These potentials must be Self-organization of periodicity hubs and spi- constant at the inner part of the billiard and present an rals in a high resolution parameter space from abrupt variation of their values at the coordinates on the the two-level model on semi-insulating GaAs, border of the billiard. Thus, the force exerted on a parti- Samir Lacerda da Silva, Instituto Federal do Esp´ırito cle subjected to this kind of potential is null into the billi- Santo - Campus Vit´oria, Rodrigo Lacerda da Silva, ard area and is infinite at the border of the billiard. Also, Instituto Federal Fluminense - Campus Bom Jesus do the direction of the force (and thus the potential gradient) Itabapoana, Emilson Ribeiro Viana, Universidade must be normal to the frontier of the billiard. In this work Tecnol´ogica Federal do Paran´a Semi-insulating Gal- we obtained a soft version of a two-dimensional billiard. lium Arsenide (SI-GaAs) samples experimentally show, Differently from the hard billiard, the particle confined under high electric fields and even at room tempera- in the soft billiard suffers the influence of a force during ture, negative differential conductivity in N-shaped form a time interval greater than zero. Due to this reason, the (NNDC). In recent work [1], we proposed a physical mo- particle trajectory is smooth at the reflections and differs del, the two-valley model, which describes electrical con- from straight lines between consecutive reflections. The duction in SI-GaAs. The model is based on the minimal obtaining of the soft billiard was made considering a par- set of generation-recombination (g-r) equations for two ticle subjected to a two-dimensional potential with a pa- valleys inside of the conduction band, and an equation rameter capable to change the values of gradient function for the drift velocity as a function of the applied elec- without however alter the shape of equipotential curves. tric field, that covers the physical properties of the non- With this, we can investigate the continuous transition linear electrical conduction of the SI-GaAs system. The of the dynamics from soft two-dimensional potential to model generated theoretically the NNDC region for the the corresponding hard two-dimensional billiard. We opt first time and the nonlinear dynamics were investigated to perform this investigation considering the elliptical ge- in this region by building of high-resolution parameter- ometry of the equipotential curves, where the values of space of the periodicity using a Periodicity-Detection rou- eccentricities are the same for each equipotential and can tine [2]. In the parameter-space we observed too many be controlled by a parameter in the potential expression. self-organized periodic structures embedded in the cha- Using this procedure we can reveal the changes of the otic regions, like as a “shrimp”shaped in a spiral form, numerical results by varying the hardness of the border that forms a “snail shell”. This structure established until recover the well known phase space of hard ellip- a direct communication between the windows in order tical billiard. We investigate the two-dimensional space within chaotic regions, producing new routes of bifurca- of parameters identifying the transitions order-chaos in tion. The snail structure show three regions where the there. ENFE - 02/11/2015 - Abstracts 15
[02/11/2015 - P047] the financial support of FAPESP (grants 2014/07043-0 Three unequal masses on a ring and soft triangu- and 2011/19296-1). lar billiards, Hercules A. Oliveira, Universidade Tecnol´ogica Federal do Paran´a, Ponta Grossa, Marcus [02/11/2015 - P049] W. Beims, Universidade Federal do Paran´a Collisions Chaos in 3D Brans-Dicke Model, with hard (infinite) walls in billiards systems are usually Thiago Gilberto do Prado,Hercules´ Alves described by instantaneous reversal of the particles linear de Oliveira Junior, Marcos Cesar Verges,` Uni- momentum. From this, simple analytical relations of ve- versidade Tecnol´ogica Federal do Paran´a The evidence locities and angles before and after the collisions with of an accelerated expansion of the universe, observed by the walls are obtained. However, in order to analyze the WMAP, opened the discussion of the general relativity transition to soft walls, which are more realistic, it is es- eventual limits. There are many options for alternative sential to have well defined equations of motion since, theories of gravity, and among them wecan cite scalar- in general, no simple analytical solutions are obtained. tensor theories like supergravity, Kaluza-Klein theories, The present work suggests that appropriated soft walls dual string theories, M-Theory, etc . One particular potentials are those for which the corresponding forces kind of scalar-tensor theory to describe an accelerate become “delta functions”in the limit of hard walls. This expansion of the universe, called Brans-Dicke theory, was allows for better numerical investigation of the soft-hard proposed in the early sixties. This theory uses the princi- transition. A general scaled Hamiltonian is derived for ple of Mach and the hypothesis of Dirac, considering an three unequal masses interacting particles on a friction- eventual variation in time of the Newton’s gravitational less ring, which nicely describes the transition and shows constant, thus ensuring the universality of free fall that the dynamics occurs inside a soft triangular billiard. (equivalence principle). Most of the works which have The dynamics of three soft interacting particles on a ring been published in this theory up to now consider four is shown to correspond to the motion of one particle in- flat dimensions, and some of them have tried to associate side a soft triangular billiard. The dynamics inside the the scalar field of the Brans-Dicke theory as quintessence soft billiard depends only on the masses ratio between field as a type of K-essence field. Others have tried to particles and softness ratio of the particles interaction. find a solution for the observed accelerated expansion The transition from soft to hard interactions can be ap- using a dimensional reduction of the 5D Brans-Dicke propriately explored using potentials for which the cor- theory without matter. Concerning 3 dimensions, a responding equations of motion are well defined in the broad study has been done in gravitational theories since hard wall limit. Numerical examples are shown for the the publication of BTZ Black Hole, motivated by the soft Toda-like interaction and the error function. fact that 3D theories avoid some complications found in higher dimensions. However, there are not as many [02/11/2015 - P048] results about 3D scalar-tensor theories, and it would Plasma Structures in Texas Helimak, be interesting to find some results in this subject, more F. A. C. Pereira, Z. O. Guimaraes-Filho,˜ I. specifically in 3D Brans-Dicke theory. For instance, we L. Caldas, Instituto de F´ısica da Universidade de S˜ao can see some problems like the association of the scalar Paulo, D. L. Toufen, Instituto Federal de Educa¸c˜ao, field of the Brans-Dicke theory to K-essence fields which Ciˆencia e Tecnologia de S˜ao Paulo, Campus Guarulhos, models the dark energy. The goal in this paper is study K. W. Gentle, Institute for Fusion Studies of the the dynamical behavior of a 3D Brans-Dicke model. For University of Texas at Austin Intermittent structures this we use tools such as calculation of the exponent with extreme events (bursts) have been detected in the Lyaponov and analysis of phase space for the study of turbulence of the scrape of layer (SOL) of Tokamaks this dynamic system. From the results we identified and these structures have a major role in plasma confi- regions whose theory has chaotic behavior. nement. The Texas Helimak is a toroidal plasma device with one-dimensional equilibrium, magnetic curvature [02/11/2015 - P050] and shear, thus resembling closely a SOL of a Tokamak. Algebraic period 3 orbits: rotation on The Texas Helimak vacuum vessel has a rectangular complex plane and statistical quantities., cross section with 0.6 m of internal radius, 1.6 m of Antonioˆ Joao˜ Fidelis´ , IFC - Campus Luzerna, Lu- external radius, and 2 m of height and the plasma ciano Camargo Martins, UDESC - CCT For the is generated by electron cyclotron resonance heating. period-3 window of the logistic map xn+1 = rxn(1 xn) The Helimak has 16 bias plates, where a large set of it is presented algebraic orbits, for both stable− and Langmuir probes is mounted and from where is possible unstable ones. From the solution of xn+3 = xn it is to impose an external electrical bias. This electrical bias obtained the polynomial that rules the periodic orbits can change the turbulence properties and even suppress inside this window. The roots of this polynomial are the appearance of the intermittent structures. In this the orbits, and they are functions of the fixed parameter work, we study the statistical characteristics of bursts value r. As r is increased, the value of the roots are in the ion saturation current, and we show that a shot modified: some increase and the others decrease. For the noise model can reproduce the signal statistics. We also same branch of the three possible orbits, the value of the characterize both the spacial and temporal profiles of roots present opposite behavior with respect to stable the bursts and their propagation, as a function of the and unstable orbits. The roots of the polynomial, i.e., external imposed bias and the radial position inside the orbits, are presented in two different ways: a sum the Helimak. Both profiles and the bursts propagation of complex numbers xi = a + bc + bc, and via Euler’s are analyzed by conditional analysis and the cross formula xi = a + 2 b cos(θ) – the overbar indicates correlation between the probes signals. We acknowledge complex conjugation.| The| algebraic orbits are obtained 16 Abstracts - ENFE - 02/11/2015 for three different fixed control parameter values of r: 2t and height 2b, as usual, we set b = 1 [1]. Here, we at tangent bifurcation (birth), at super-stability and study numerically the vicinity of a particular line in the at ending pitchfork bifurcation (death). The algebraic paramater space a t, namely t = t (a) = √a2 1. If × c 0 − expressions of the constants a, b, c, b and θ are given t > tc, there is chaos almost everywhere[1]. If t Oral sessions (11:00-12:30) non-standard reservoirs, we introduce the concept of temperature of n-th order to characterise the typical scale of energy that is represented by the n-th order FUNDAMENTAL ASPECTS cumulant of the noise. With that concept in hand, we also analyse the form of the large deviation function of [02/11/2015 - 11:00 - Room Tubar˜ao] the energy fluxes and fluctuation relations in systems of Nonperturbative renormalization group for the this kind. Kardar-Parisi-Zhang equation, Leonie´ Canet, [02/11/2015 - 11:35 - Room Tubar˜ao] Universit´eJoseph Fourier Grenoble I, Hugues Chate,´ Stochastic thermodynamics, Taniaˆ Tome,´ CEA, Service de Physique de lEtat Condens´e, Gif- Mario´ J. de Oliveira, Instituto de F´ısica, Universi- sur-Yvette, France, Bertrand Delamotte, LPTMC, dade de S˜ao Paulo We develop the stochastic appro- Paris 6, Paris, France, Thomas Kloss, CEA, Ins- ach to thermodynamics based on the stochastic dynamics, titut de Physique Th´eorique, Gif-sur-Yvette, France, which can be discrete or continuous, and on two assump- Nicolas´ Wschebor, Universidad de la Rep´ublica, tions concerning entropy. In the discrete case, the system Montevideo, Uruguay We present a method, rooted in is governed by master equation and in the continuous the non-perturbative renormalization group, that allows case, by a Fokker-Planck equation. The first assumption one to calculate the critical exponents and the correlation concerns the definition of entropy, which is taken to be the and response functions of the Kardar-Parisi-Zhang(KPZ) Boltzmann-Gibbs entropy, and thus has the same form as growth equation in all its different regimes, including the the equilibrium definition. The difference is that the pro- strong-coupling one. We implement an approximation bability distribution may be time-dependent. The second scheme and show that it yields a complete, qualitatively assumption has to do with the definition of entropy pro- correct phase diagram in all physical dimensions with re- duction rate, which is taken to be the expression intro- asonable values for the critical exponents. We also com- duced by Schnakenberg. This expression is nonnegative pute in one dimension the full (momentum and frequency by definition and vanishes in the thermodynamic equili- dependent) correlation function, and the associated uni- brium. Based on these assumptions we study interacting versal scaling functions. We find an excellent quantita- systems with many degrees of freedom in equilibrium or tive agreement with the exact results from Praehofer and out of thermodynamic equilibrium, and how the macros- Spohn (2004). This result is generalized in 2+1 en 3+1 copic laws are derived from the stochastic dynamics. In predicting correlation and response functions. Associa- particular, we will discuss the quasi-static processes de- ted universal amplitude ratios were predicted and have fined as the ones in which the thermodynamic fields are after been successfully confirmed by lattice simulations varied slowly. We show that the rates of energy, entropy (Halpin-Healy, 2013). Generalizations as the inclusion and number of particle, are linear in the rate of the ther- of anisotropies or long-range correlated noise are discus- modynamics fields whereas the production of entropy is sed. Finally, preliminary results in order to improve the quadratic in these rates so that it may be negected and approximation in order to analyze the four and higher di- the system may be considered to be in thermodynamic mensional behavior is also discussed. The presented work equilibrium. We show that along a quasi-static process is based on the references Phys. Rev. Lett. 104 (2010) the representative point in the space energy, entropy and 150601; Phys. Rev. E84 (2011) 061128; Phys. Rev. E86 number of particle, remains on a surface and that this (2012) 051124; Phys. Rev. E89 (2014) 2, 022108; Phys. surface has the property of convexity. Rev. E90 (2014) 6, 062133, [02/11/2015 - 11:50 - Room Tubar˜ao] [02/11/2015 - 11:20 - Room Tubar˜ao] Exact solution for a 1+1 etching model, Washing- What is a n-th order temperature?, ton S. Alves, Bernardo A. Mello, Ismael V. S´ılvio M. Duarte Queiros´ , CBPF, Welles A. L. Costa, Fernando A Oliveira, Universidade M. Morgado, PUC-Rio Although a huge stake of de Bras´ılia - UnB We present a method to derive problems in non-equilibrium statistical mechanics is analytically the growths exponents of a surface of related to thermal reservoirs that within the context 1 + 1 dimensions whose dynamics is ruled by cellular of a Langevin description are described by Gaussian automata. Starting from the automata, we write down noises, there is an important set of problems - which go the time evolution for the height’s average and height’s from diffusive motion in little dense media to molecular variance (roughness). We apply the method to the motors powered by exergonic chemical reactions such as etching model [1,2,3,4] than we obtain the dynamical the hydrolysis of ATP - for which the stochastic nature exponents, which perfectly match the numerical results of the noise in the dynamical equations ought to be obtained from simulations. Those exponents are exact everything but Gaussian. As a matter of fact, most of and they are the same as those exhibited by the KPZ those systems are very well described by taking into model [5] for this dimension. Therefore, it shows that consideration Poissonian shot-noise terms for mimicking the etching model and KPZ model belong to the same the interaction system-reservoir. If, to a good extent, universality class [6]. it is possible to map athermal linear systems into standard reservoir cases by means of defining a canonical [1] B. A. Mello, A. S. Chaves, and F. A. Oliveira, Phys. temperature, the existence of non-linearities puts the Rev. E 63, 041113 (2001). singular nature of a shot-noise reservoir in the limelight. [2] E. A. Rodrigues, B. A. Mello, and F. A. Oliveira, J. In that case, specious violations of the principles of Phys. A 48, 035001 (2015). thermodynamics can emerge. Aiming to reconcile such [3] F. D. A. Araao Reis, Physica A 364, 190 (2006). natural principles with the analytical properties of [4] Z. Xun, Y. Zhang, Y. Li, H. Xia, D. Hao, and G. Tang, 20 Abstracts - ENFE - 02/11/2015 J. Stat. Mech. 10, 0014 (2012). nonuniform transition rates. The steady state chemical [5] M. Kardar, G. Parisi, and Y. C. Zhang, Phys. Rev. potential profile is, moreover, nonuniform at coexistence, Lett. 56, 9, 889 (1986). contrary to the basic principles of thermodynamics. [6] W. S. Alves, B. A. Mello, H. A. Fernandes, F. A. As a further example, I discuss examples of a pair of Oliveira and I. V. L. Costa to be published. systems possessing identical steady states, but which do [02/11/2015 - 12:05 - Room Tubar˜ao] not coexist when placed in contact. I then turn to the Entropic Inference and Backward Renormaliza- question of phase coexistence in nonequilibrium steady tion Group priors, Nestor Caticha, IF Universi- states. Results on the driven lattice gas with attractive dade de S˜ao Paulo Maximum Entropy inference (ME) interactions show that the bulk densities of coexisting is a unique inference engine. Starting from prior distri- phases are different for phases that (1) separate spon- butions, codifying previously available information, ME taneously in a single inhomogeneous system, and (2) permits the update to new probability distributions, in- phases that coexist under particle exchange between corporating information as it becomes available. Its ever two homogeneous systems. These results cast serious expanding scope of applications fuels the need to improve doubt on the consistency and predictive value of SST, the construction of informative priors that lead to impro- and on the notion of thermodynamic phases far from ved inferential results. In this paper we are interested in equilibrium. general inverse problems which can benefit from a mul- [02/11/2015 - 11:20 - Room Vit´oria] tiscale approach. We construct a systematic method of Phase transitions in non-equilibrium stationary transferring information from coarser to finer resolutions states driven by multiplicative stochastic proces- based on Renormalization Group transformations. It per- ses, Daniel G. Barci, Miguel V. Moreno, Depar- mits building informative priors in finer scales from pos- tamento de F´ısica Te´orica, Universidade do Estado do teriors in coarser scales. This can be done since, under Rio de Janeiro., Zochil Gonzalez´ Arenas, Departa- some conditions, Renormalization Group transformations mento de Matem´atica Aplicada, Universidade do Estado in the space of hyperparameters can be inverted. These do Rio de Janeiro Stochastic processes with multipli- are a class of Markov embeddings. These priors are then cative noise often leads to stationary out-of-equilibrium updated using renormalized data into posteriors by ME. states. They are characterized by the presence of proba- ME updating with constraints in the form of data me- bility currents and, in general, time-reversal is a broken asurements is equivalent to Bayes updating but permits symmetry and usual equilibrium properties, such as de- repited use of renormalized data at different scales. The tailed balance, are not satisfied. In this type of statio- resulting inference method, Backward RG (BRG) priors, nary states, symmetry-breaking phase transitions could is tested by doing simulations of a functional Magnetic take place, induced by noise [1]. That is, for weak noise Resonance imaging (fMRI) experiment. Its results are the stationary state is usually disordered. However, an compared with a Bayesian approach working in the finest ordered state sets in when the noise intensity is increa- available resolution. Using BRpriors sources can be par- sed. There are two necessary ingredients to produce this tially identified even when signal to noise ratio levels are class of phase transitions: multiplicative noise and out- up to 25dB improving vastly on the single step Baye- ∼− of-equilibrium stationary states. sian approach. For low levels of noise the BRprior is not In this work, we present a study on out-of-equilibrium an improvement over the single scale Bayesian method. phase transitions induced by multiplicative noise. Re- Analysis of the histograms of hyperparameters can show cently, we have presented a functional formalism [2,3]. how to distinguish if the method is failing, due to very to compute correlations functions in these systems. Ba- high levels of noise, or whether the identification of the sed on that, we built up a “dynamical potential” written sources is, at least partially possible. in terms of an order parameter capable to describe non- Acknowledgment: Presentation supported by Fapesp equilibrium phase transitions. As an example, we applied our formalism to a particu- NON EQUILIBRIUM larly simple model which captures the physics of non- equilibrium phase transition. The model is defined by a [02/11/2015 - 11:00 - Room Vit´oria] set of stochastic variables arranged in a hyper-cubic lat- Failure of Steady State Thermodynamics, tice satisfying a system of interacting Langevin equations Ronald Dickman, Universidade Federal de Minas Ge- with multiplicative noise, where we consider first neigh- rais Steady state thermodynamics (SST) is an attempt bors interactions. We computed a “dynamical potential” to extend thermodynamics to nonequilibrium steady sta- for the stationary state in the saddle-point plus Gaussian tes arbitrarily far from equilibrium, attributing intensive fluctuations approximation. From this, we have built up variables such as temperature and chemical potential to a phase-diagram in terms of the lattice interaction and these systems. To be useful, SST must be self-consistent the noise. We discovered a phase transition with reen- and have predictive value. I examine this issue in the trant behavior for sufficiently strong lattice coupling. We context of driven stochastic lattice gases. Consistency computed the phase diagram for different dimensions and of SST is verified for driven lattice gases under global for different values of the stochastic prescription that de- weak exchange, but only for a particular class transition fines the multiplicative stochastic process. At the level rates, those defined by Sasa and Tasaki. Under local of this approximation we found that the phase transition (pointwise) exchange, consistency only holds in the limit is continuous and we computed critical exponents. Even of a vanishing exchange rate. SST fails to predict the thought, the concept of universality is not completely de- coexisting densities under a nonuniform drive, or in the veloped in out-of-equilibrium transitions, the computed presence of a nonuniform density provoked by a wall or exponents are in the universality class of the dynamical ENFE - 02/11/2015 - Abstracts 21 Ising model. of weak interaction no longer holds. As a result, the iconic [1] C. Van den Broeck, J. M. R. Parrondo, R. Toral, R. spontaneous emission of photons by atoms cannot occur Kawai, Phys. Rev. Lett. 73, 3395 (1994); Phys. Rev. as N independent events, even for N = 2, as verified E55, 4084 (1997). in recent experiments. The quantum interference among [2] Zochil Gonz´alez Arenas and Daniel G. Barci, Phys. the ensemble shapes the emission in cavities. SOP are Rev. E81, 051113 (2010); Phys. Rev. E 85, 041122 also relevant in a large variety of classical problems, na- (2012); J. Stat. Mech. P12005.(2012). mely, efficient brochure dissemination in advertising and [3] Miguel V. Moreno, Zochil Gonz´alez Arenas and Daniel disease spreading by aerial vectors, such as dengue fe- G. Barci, Phys. Rev. E91, 042103 (2015) ver. Here, we present a new technique for self-organizing This work was partially supported by CNPq, CAPES and systems to evaluate high order statis- tics employing a FAPERJ. classical toy model. The technique is valid only for SOP [02/11/2015 - 11:35 - Room Vit´oria] where small fluctuations originates a rapid growth rate. Restricted permutations and random (0, 1)- The toy model considered is composed by an urn and N matrices in the symmetric simple ex- distinguishable balls, uniquely identifiable by their labels. clusion process in discrete time over Each time, a given ball is randomly selected, its label is graphs, J. Ricardo G. Mendonc¸a, EACH/USP then recorded in a list and then the ball is returned back to the urn. However, the samples are formed by counting Motivations to study exclusion processes in general and exclusion processes over graphs in particular are the number of unique labels found in a given list. This manifold. In physics, exclusion processes are simple measure process introduces correlations in time for each models that provide nontrivial results on a number of sample, which in turn triggers a collective behavior, as basic issues, such as the relaxation dynamics of a gas also reported for pulsed photon emission in the super- or fluid towards the thermodynamic equilibrium. They radiant models. In Probability Theory, this problem is are also relevant in the modeling of interacting processes also referred as the classical coupon-collector’s problem, such as queueing systems, traffic, signaling in radio and whose solution has been unveiled only recently, using the computer networks, and rumour and epidemics spreading poissonization technique. This technique hides the inte- in social networks. Moreover, exclusion processes are na- resting underlying finite sym- metries, which are relevant tural generalizations of the single random walk problem. for physical properties. Instead, the statistics in the toy The mathematics of random walks on graphs and groups model are derived here from the geometrical properties has been an active field of investigation for at least four of multidimensional Pascal triangle and are closely re- decades by now, having led to many developments in lated to counting problems. Our findings contemplate pure and applied probability, statistics, combinatorics, both small and large N limit. In addition, the mapping group theory, and harmonic analysis. In this work we between the classical toy model and superradiance per- describe the dynamics of the symmetric simple exclusion mits the formulation of new simple classical Monte Carlo process in discrete time over simple graphs by means of methods to investigate the cooperative regime in cavity suitably restricted permutations over the labels of the QED models. vertices of the graphs. Straightforward Monte Carlo [02/11/2015 - 12:05 - Room Vit´oria] and sequential importance sampling algorithms for Fluctuation of heat flow along one sampling restricted permutations inspired by the related dimensional linear conducting chain, problem of computing permanents are implemented and Welles Antonio Martinez Morgado, Michael compared. We illustrate the formalism by estimating Moraes Candido,ˆ PUC - Rio, Silvio Manuel the relaxation times of the symmetric simple exclusion Duarte Queiros,´ CBPF Anomalous conductivity is process in discrete time over Newman-Watts small-world a strong characteristic of linear chains. The main reason networks. for it is the ballistic way phonons propagate in these [02/11/2015 - 11:50 - Room Vit´oria] systems. It would be expected that non-linear systems Exact evaluation of high order statistical mo- would fix that problem due to the phonon-phonon cou- ments in self-organizing phenomena, Brenno pling present in them. However, due to their crumpled Caetano Troca Cabella, Departament of Clinical one dimensional topology, non-linearity is not suffici- Neurosciences, University of Cambridge, Cesar Au- ent to effectively diffuse heat under non-equilibrium gusto Sangaletti Terc¸ariol, Centro Universit´ario conditions, namely under distinct temperatures at its Bar˜ao de Mau´a, Gilberto Medeiros Nakamura, extremities. Indeed, it is well known that even non-linear Alexandre Souto Martinez, Universidade de S˜ao higher dimensional systems do not satisfy Fourier law as Paulo Self-organizing phenomena (SOP) are ordered well. collective behavior that arises from small fluctuations and The one dimensional model is thus a source of intriguing develops positive feedback. These collective effects are anomalies that might be of interest due to its applicability macroscopically observable and are governed by higher to experimental nano-scale systems such as nano-wires, order statistical moments and correlation functions. An nanotubes (as objects that make the crossover between interesting example of the SOP role as the underlying 1D and 2D), and many more. In fact, thermal properties Physics is the atomic superradiant emission of photon in for these systems are still quite hard to access experimen- cavities. This effect emerges from the interaction of a sin- tally. gle quantum electromagnetic field with N emitters, each The use of classical models might give us insight on some modeled as a two-level system, trapped inside an optical of the more important properties for these systems. The cavity. When the typical distance between atoms is smal- heat flux has already been extensively studied for them, ler than the emitted photon wavelength, the assumption in special how to eliminate the anomalous behaviour men- 22 Abstracts - ENFE - 02/11/2015 tioned earlier and make them obey Fourier Law. Several Oral sessions (14:30-16:05) techniques have been developed such as self-consistent thermal reservoirs along the chain, effective interacti- ons with external particles, and mass dispersion among EPIDEMICS & CELL GROWTH others. However, higher moments of the heat flux have not been [02/11/2015 - 14:30 - Room Vit´oria] extensively explored despite the fact that they bring im- Biological populations and epidemic spreading: portant information about the organization of the energy stochastic and spatially structured modeling, transport throughout the chain. Taniaˆ Tome´, Instituto de F´ısica - USP We will ad- In this spirit, we have studied them by means of exac- dress topics covered by the stochastic dynamics, which tly solving the coupled Langevin equations that define are inserted in the field of statistical physics of non- the dynamics of the system. We have found interesting equilibrium. The issues we will fix concern the modeling properties, such as the non-dependence of chain length of biologically motivated systems. Topics to be visited for the transmission of higher order fluctuations. We are consist primarily those related to the dynamics of biolo- going to report on these results and show how they are gical populations as well as those related to spread of epi- necessary to form a complete and consistent picture of demics. To this end, we will consider irreversible models heat conduction for the harmonic chain. described by a Master equation and probabilistic cellu- lar automata. Among the epidemic models to be discus- sed are: the Susceptible-Infected-Recovered system (SIR) described by a master equation; and a model to describe the stochastic dynamics for dengue epidemic. Among the models for biological populations is a stochastic lattice model to describe the coexistence of predators and prey in a habitat. This coexistence may be accompanied by fluc- tuations in the populations of each species. We will talk over the nature and characterization of these oscillations. We intend to explore the spatiotemporal patterns rela- ted to population dynamics. In addition, we analyze the dynamical and static critical behavior and universality classes associated to non-equilibrium phase transitions, which may occur in these systems. References (1)Tˆania Tom´eand M. J. de Oliveira, Stochastic Dynamics and Irreversibility, Springer, 2015. (2)D. R. de Souza, Tˆania Tom´e, S. Pinho and F. Barreto, Phys. Rev. E 87, 012709 (2013). (3)Tˆania Tom´eand R. M. Ziff, Phys. Rev. E 82 051921 (2010). (4)T. Tom´e, A. L. Rodrigues, E. Arashiro and M. J. de Oliveira, Comput. Phys. Comm 180, 536 (2009). [02/11/2015 - 14:50 - Room Vit´oria] Multiple transitions of the susceptible-infected- susceptible epidemic model on complex networks, Angelica´ Sousa da Mata, Universidade Federal de Lavras, Silvio da Costa Ferreira Junior, Univer- sidade Federal de Vi¸cosa Phase transitions involving equilibrium and nonequilibrium processes on complex networks have begun drawing an increasing interest soon after the boom of network science in the late 1990s. Per- colation, epidemic spreading, and spin systems are only a few examples of breakthrough in the investigation of cri- tical phenomena in complex networks. Absorbing state phase transitions have become a paradigmatic issue in the interplay between nonequilibrium systems and com- plex networks with epidemic spreading being a prominent example where high complexity emerges from very simple dynamical rules on heterogeneous substrates. The exis- tence or absence of finite epidemic thresholds involving an endemic phase of the susceptible-infected-susceptible (SIS) model on scale-free networks with a degree distri- γ bution P (k) k− , where γ is the degree exponent, has been target of∼ a intense investigation. Distinct theoreti- cal approaches for the SIS model were devised to deter- mine an epidemic threshold λc separating an absorbing, disease-free state from an active phase. The quenched ENFE - 02/11/2015 - Abstracts 23 mean-field (QMF) theory explicitly includes the entire [02/11/2015 - 15:20 - Room Vit´oria] structure of the network through its adjacency matrix Assessing the International Spreading Risk As- while the heterogeneous mean-field (HMF) theory per- sociated with the 2014 West African Ebola Out- forms a coarse-graining of the network grouping verti- break, Marcelo F C Gomes, PROCC/FIOCRUZ ces accordingly their degrees. The HMF theory predicts - RJ - Brasil, Ana Pastore y Piontti, Alessan- a vanishing threshold for the SIS model for the range dro Vespignani, Northeastern University - EUA, Luca 2 <γ< 3, while a finite threshold is expected for γ > 3. Rossi, ISI Foundation - It´alia, Dennis Chao, M. Eli- Conversely, the QMF theory states a threshold inversely zabeth Halloran, Fred Hutchinson Cancer Research proportional to the largest eigenvalue of the adjacency Center - EUA, Ira Longini Jr., University of Florida matrix, implying that the threshold vanishes for any va- - EUA Background: The 2014 West African Ebola lue of γ. For γ < 3, there exists a consensus for SIS Outbreak is so far the largest and deadliest recorded in thresholds. However, for γ > 3 the different mean-field history. The mainly affected countries, Sierra Leone, Gui- approaches predict different outcomes. Therefore, in this nea, Liberia, have struggled to contain and to mitigate work, we performed extensive simulations in the quasis- the outbreak. After more than one year from the rise in tationary state of the SIS dynamics on random networks transmission, the latest WHO report finally showed the having a power law degree distribution with γ > 3, for lowest total number of weekly cases since March 2014. a comparison with these mean-field theories. We obser- Up to August 2nd, 2015, a total of 27898 confirmed, ved concomitant multiple transitions in finite networks probable, and suspected EVD cases have been reported presenting large gaps in the degree distribution and the worldwide, of which 11296 died. Aside from most affected obtained multiple epidemic thresholds are well described countries in West Africa, a total of 7 other countries have by different mean-field theories. We observed that the had imported cases, reaching 3 continents: Africa (Nige- transitions involving thresholds which vanish at the ther- ria, Senegal and Mali), Europe (Italy, Spain and the UK) modynamic limit involve localized states, in which a va- and North America (the USA). nishing fraction of the network effectively contributes to Method: We used the Global Epidemic and Mobility Mo- epidemic activity, whereas an endemic state, with a fi- del to generate stochastic, individual based simulations of nite density of infected vertices, can occur at a finite th- epidemic spread worldwide, yielding, among other measu- reshold. res, the incidence and seeding events at a daily resolution Acknowledgements and Financial Support: FAPEMIG, for 3,362 subpopulations in 220 countries. The mobility CAPES and CNPq. model integrates daily airline passenger traffic worldwide and the disease model includes the community, hospital, [02/11/2015 - 15:05 - Room Vit´oria] and burial transmission dynamic. We use a multimodel SIMULATION OF AN EPIDEMIC MO- inference approach calibrated on data from the month of DEL WITH VECTOR TRANSMISSION, August 2014. The estimates obtained were used to ge- Adriana Gomes Dickman, Pontif´ıcia Universidade nerate monthly ensemble forecasts that provided quanti- Cat´olica de Minas Gerais, Ronald Dickman, Univer- tative estimates of the local transmission of Ebola virus sidade Federal de Minas Gerais We study a lattice disease in West Africa and the probability of international model for vector-mediated transmission of a disease in spread if the containment measures were not successful a population consisting of two species, A and B, which at curtailing the outbreak. Results were posted in near contract the disease from one another. Individuals of real-time to help public health authorities decision ma- species A are sedentary, while those of species B (the king. We also tested the impact of on-site intervention vector) diffuse in space. Examples of such diseases are measures in the local spread and importation probability. malaria, dengue fever, and Pierce’s disease in vineyards. Results: We model the short-term growth rate of the There are several ways of interpreting the model: A disease in the affected West African countries and esti- contact process (CP) on the A population, mediated by mate the basic reproductive number. We simulated the B; a diffusive epidemic process (DEP) on the B popu- international spreading of the outbreak and provide the lation, mediated by A; or a multicomponent epidemic estimate for the probability of Ebola virus disease case process in which B and A are equally essential. The importation in countries across the world, including in- model exhibits a phase transition between an absorbing tervention scenarios. (infection free) phase and an active one as parameters such as infection rates and vector density are varied. [02/11/2015 - 15:35 - Room Vit´oria] We study the static and dynamic critical behavior of Cell sorting with variable cluster size: the model using initial spreading, initial decay, and a Smoluchowski equation approach, quasistationary simulations. Although phase transitions Carine Priscila Beatrici, Rita Maria Cunha to an absorbing state fall generically in the directed de Almeida, Leonardo Gregory Brunnet, IF- percolation (DP) universality class, this appears not UFRGS Cell segregation is an widespread phenomena to be the case for the present model. Our preliminary in nature and has interested physicists since the last results clearly exclude DP scaling for the parameter 50 years. It opens the possibility of studying a system values studied. Compatibility with DEP scaling remains composed of many interacting active identical elements, an open question. Our results raise the possibility both theoretically and experimentally. A typical cell of two phase transitions in the epidemic model with sorting experiment measures the evolution of clusters vector transmission, as at the apparent critical point for sizes, or also the size of the interface between the two survival in spreading and quasistationary behavior, the tissues at stake. The dynamics underlying cell migration number of infected individuals in spreading simulations drives the cell segregation, which is directly related n(t) grows more slowly than a power law. to cluster formation, where the endoderm cells attach 24 Abstracts - ENFE - 02/11/2015 each other forming groups. This development evolves documents or a device as proof of identification. The through cluster diffusion and depends on cluster cross formation of signature varies from person to person or section and cell affinity. In the context of active media even from the same person due to the psychophysical cluster growth may present unexpected exponents when state of the signer and the conditions under which the compared to non-active matter. When clusters are signature apposition process occurs. Handwritten sig- formed by inert particles it is expected that the diffusion nature characterization and verification is a behavioral scales inversely with the cluster mass, in the case of biometric modality that relies on a rapid personal ges- active matter that does not hold and this is central ture. Each hand-drawn signature has a level of comple- to define the segregation time scales. Also, finite size xity which depends on the author. Among all the bio- effects are important since they impose deviation from metric traits that can be categorized as pure behavioral, power law solutions. To approach this problem from the signature is the one that has the widest social accep- a theoretical point of view we use the Smoluchowski tance for identity authentication. Online signature verifi- fragmentation-coagulation equation with an adapted cation allows the introduction of the signature’s dynamic coagulation kernel and a fragmentation kernel. It is information, not just the outcome of the signing process. found that the underlying growth power laws may be Such dynamical information is captured by a digitizer, hidden depending on initial cluster sizes, sample size and generates “online”signatures, namely a sequence of and fragmentation constant. The average cluster size sampled points during the signing process: x, y (t), the solutions found with the Smoluchowski equation are coordinate x and y at time t. We compute Information- used to fit the data resulting from the simulations and Theoretic measures (Shannon Entropy, Generalized Sta- the power law behavior can be clearly separated out of tistical Complexity and Fisher information measure), on the minimum and maximum cluster size limits. the Bandt-Pompe nonparametric descriptor, which take [02/11/2015 - 15:50 - Room Vit´oria] into account the time causal of the corresponding time Cell Segregation and Group Diffusion, series. These measures are used as the input features of a Carine Beatrici, Rita M. de Almedia, signature characterization and verification system, whose Leonardo G. Brunnet, Universidade Federal do performance is assessed over the well known MCTY 100 Rio Grande do Sul The dynamics underlying cell signature data base. Our results are competitive in terms migration drives cell segregation which is essential to of acceptance and rejection errors, and is shown very at- tissue formation. Since the mid-twentieth century a tractive in terms of computational requirements. series of hypotheses for the microscopic mechanism [02/11/2015 - 15:05 - Room Tubar˜ao] were put to test to explain the evolution observed in Nonstationarities and sleep disturbance detec- experiments. A typical experiment in cell segregation tion, Sabrina Camargo, Escola de Matem´atica measures the evolution of clusters sizes, or also the size Aplicada, Funda¸c˜ao Get´ulio Vargas, Celia Antene- of the interface between the two tissues at stake. In odo, Departamento de F´ısica PUC-Rio, Maik Riedl, order to appropriately fit the experiment a series of Jurgen¨ Kurths, Niels Wessel, Humboldt Universit¨at physical constraints must be taken into account, such zu Berlin We present recent results on sleep apnea- as the finite size of each cell, the finite number of cells hypopnea quantification. Sleep apnea is the most com- in the process and the scaling of the cluster diffusion mon sleep disturbance and it is an important risk factor with its mass. Here we explore a mean cluster approach for cardiovascular disorders. The diagnostic is obtained that explicitly includes these constraints. In some trough combined exams, and we aim to offer an alterna- appropriate limits this mean cluster approach has exact tive procedure. A sleep apnea event is defined as a break solutions with simple power laws with finite size effects in the airflow that lasts at least 10 secs. If the air flow is clearly identified. Simulations of cell segregation based less than 50% of normal, the resulting airflow limitation is on the differential adhesion hypothesis are implemented called hypopnea. Individuals who suffer from this kind of using simple active matter models. The mean cluster disorder usually present daytime sleepiness, loud snoring approach solutions are used to fit the data resulting and restless sleep. Blood pressure, heart rate variability, from the simulations and the power law behavior can respiratory variability, and other cardiorespiratory data be clearly separated out of the minimum and maximum could be useful to detect sleep disturbances, and it is cluster size limits. The relation found between the group important to emphasize that cardiorespiratory time se- diffusion with its mass and the preferential alignment of ries are highly nonstationary, which restricts the use of cell velocities inside clusters impact on the power law standard tools of time series analysis. Hence, we apply a exponents with direct consequences to the segregation nonparametric segmentation procedure to yield patches time scales. where stationarity is verified. Within each of these locally stationary data segments, the statistical moments of the TIMESERIES signal, such as mean and variance, remain constant. Seg- mentation also provides the intrinsic time scales, through [02/11/2015 - 14:50 - Room Tubar˜ao] the duration of segment lengths. We show that the occur- Handwrite signature characterization and veri- rence of sleep apnea events can be quantified by means fication using time causal Information Theory of blood pressure time series analysis, and by comparing quantifiers, Osvaldo Anibal Rosso, Raydonal local quantities to an apnea score previously obtained by Ospina, Alejandro Frery, Instituto de F´ısica, Uni- polysomnographic exams, we propose an apnea quantifier versidade Federal de Alagoas, Macei´o, Brasil A sig- based on blood pressure signal with an accuracy of 82%. nature is a handwritten depiction of someone’s name or Ref: S. Camargo, M. Riedl, C. Anteneodo, J. Kurths, T. some other mark of identification that person writes on Penzel, N. Wessel, Sleep apnea-hypopnea quantification ENFE - 02/11/2015 - Abstracts 25 by cardiovascular data analysis, Plos One 9, e107581 ONI, were verifying by Cross-Sample Entropy analysis of the series. The results point to the existence of a climate [02/11/2015 - 15:20 - Room Tubar˜ao] system with climate dynamic regulation of low dimen- New Features on Gradient Pattern sional and presence of deterministic chaos. The tempo- Analysis of Extended Complex Systems, ral evolution of nonlinear parameters obtained present a Reinaldo Roberto Rosa, Rubens Sautter, complex dynamics that may have related and influence LAC-INPE-MCTI Quantitative characterization of of the fluctuations in ONI index. spatio-temporal patterns is clearly essential to the Keywords: Complex dynamics, Air temperature, Oceanic understanding of spatio-temporal phenomena. An im- Ni˜no Index. portant question in this problem concerns the long-term evolution of the pattern properties. Usually, the classical [02/11/2015 - 15:50 - Room Tubar˜ao] measures of complex extended variability do not take Light with tunable non-Markovian phase into account the directional information contained in imprint, Robert Fischer, CPGEI, Univer- a vectorial field: the main source of spatio-temporal sidade Tecn´ologica Federal do Paran´a, Itamar variability. Moreover, since spatio-temporal information Vidal, DF - Universidade Federal da Para´ıba, is even more accessible through high resolution digitized Ana Carolina Ribeiro-Teixeira, Universidade images, the need for sensitive techniques working in the Federal de Ciˆencias da Sa´ude de Porto Alegre, Ricardo real space is evident In this context, Gradient pattern R. B. Correia, Sandra D. Prado, Jandir M. analysis (GPA)[1] is a geometric computing method for Hickman, Instituto de F´ısica - Universidade Federal characterizing geometrical bilateral symmetry breaking do Rio Grande do Sul, Doron Gilboa, Yaron Sil- of an ensemble of symmetric vectors regularly distributed berberg, Department of Physics of Complex Systems, in a square lattice. The measures obtained from GPA Weizmann Institute of Science Designing the spatial are based on the spatio-temporal correlations between coherence properties of light is fundamentally important large and small amplitude fluctuations of the structure to most applications in optics and photonics. Usually, represented as a dynamical gradient pattern. By means efforts are made to increase the light’s spatial coherence, of four gradient moments it is possible to quantify through spatial filtering, for instance. However, for some the relative fluctuations and scaling coherence at a applications, like the generation of random numbers dynamical numerical lattice and this is a set of proper or patterns, the opposite is desired. When the light measures of the pattern complexity and equilibrium. spatial coherence length is smaller than the detection Taking into account massive gradient fields (N > 104 unit (e. g. the pixel size of a CCD camera), then the vectors) In this talk we describe new features on how intensity measured at each pixel is uncorrelated to any to compute the gradient moments based only on the other pixels. This is the case of thermal light, usually phase portrait of bilateral symmetry breaking computed modeled as delta-correlated. Moreover this is the spatial into the GPU/CUDA paradigm. Examples of this new analogue of a temporal Markovian process. In this work approuch for big data is performed on Chaotic Coupled we explore for the first time a spatial phase imprint Map Lattices and also on gravitational N-body systems analogue of a non- Markovian process inspired in the for cosmological large structure formation. Sudoku puzzle. [1] Rosa et al. Physica A, 386:366-673, 2007. doi : Sudoku puzzles are a suitable basis for such conditional 21 10.1016/j.physa.2007.08.044 randomness in 2D: the fact that only 6.67 10 out of 9 9 77 × the total 9 × 1.96 10 configurations are possible ≃ × [02/11/2015 - 15:35 - Room Tubar˜ao] solutions provides a measure of randomness, while the Cross-Sample Entropy Analysis for Climate Data, Sudoku rules (in each column, row and 9 9 block the S. T. Silva, Instituto Federal de Educa¸c˜ao, Ciˆencia e numbers 1 to 9 can only be used once)× provide strict Tecnologia de Mato Grosso, S. R. Paulo, Unversidade constraints to this randomness. Federal de Mato Grosso, Instituto de F´ısica Currently Sudoku light can be experimentally generated by phase due to intense modification of the natural environment imprinting a conditional random pattern on a planar wa- and global climate change, many researches has been mo- vefront via a spatial light modulator, for which the phases tivated to investigate relationships between El Ni˜no phe- of different points in the beam profile are generated using nomena dynamics and climatological variables. Unders- a Sudoku solver. tanding the dynamics that govern the climate can be done We solve overlapping Sudoku puzzles for a large area through analysis of nonlinear dynamical systems because (e.g. 1024 1024) and apply the resulting pattern as the phenomenon involved has chaotic behavior. The re- phase imprint× on a Gaussian light beam. Simulations construction of the system dynamics that originated the show that such light, when focused, displays a symmetric possible climate changes patterns, with only one measu- pattern with a centric cross-shaped minima. Further- rement scale, it is possible, through specific techniques of more, we note that the diffraction pattern of the light time series analysis. The description of the level of com- after a double slit does neither correspond to coherent plexity or irregularity of time series can be made through nor to incoherent thermal light, but rather shows fringes the analysis of their Cross-Sample Entropy.The study was in the outer lobes while having a minimum at the place conducted with data from the meteorological station of of the zero’s order. These counterintuitive properties of Cuiab´a, provided by INMET (National Institute of Mete- Sudoku light, while violating the spatial equivalent of orology) through of BDMEP (Meteorological Data Bank the Markovian condition, may have some applications for Education and Research) in the 1961-2013 periods. in the context of decay and initialization of quantum The evidence of a possible connection between air tem- states. perature dynamic states and the Oceanic Ni˜no Index - 26 Abstracts - ENFE - 02/11/2015 References: Oral sessions (17:05-18:15) Robert Fischer, Itamar Vidal, Doron Gilboa, Ricardo R. B. Correia, Ana Carolina Ribeiro-Teixeira, Sandra D. Prado, Jandir M. Hickman, Yaron Silberberg, accepted FUNDAMENTAL ASPECTS for publication in Physical Review Letters. [02/11/2015 - 17:05 - Room Tubar˜ao] A Modern Approach to Computational Simula- tion of Phase Transitions., Costa BV, Departa- mento de Fisica - UFMG A phase transition is one of the richer and beautiful phenomenon observed in na- ture. The transformation of ice in water and water in gas, the spontaneous magnetization of a piece of iron or the spontaneous symmetry breaking during the big bang are a few examples of phase transition. Several techni- ques were developed to treat phase transitions. An ex- perimenter measures the effects in his laboratory and a theorist make the necessary approximations to provide general aspects of that specific model. In this talk we will approach the problem from a different perspective. In fact a perspective more adequate to the XXIst Cen- tury. We will use computational techniques or to be more exact ”COMPUTATIONAL SIMULATION”. Although the technique has appeared for the first time in the mid- dle of the last century, only now it is being recognized as a new branch of the languages used to understand nature. Much of this recognition is due to the fast development of new computers (In the hexaflops nowadays) and to the development of new algorithms. In this lecture I will give an introduction to the Monte Carlo techniques: Metro- polis, Single Histograms and Wang-Landau, as well as an analysis of phase transitions using the Fisher Zeros. [02/11/2015 - 17:25 - Room Tubar˜ao] Signatures of the Berezinskii-Kosterlitz-Thouless transition in the location of the zeros of the ca- nonical partition function for the 2D XY-model, J.C.S. Rocha, L.A.S. Mol,´ B.V. Costa, Universi- dade Federal de Minas Gerais In this work we show how one can use the zeros of the canonical partition func- tion, the Fisher zeros, to unambiguously characterize a transition as being in the Berezinskii-Kosterlitz-Thouless (BKT ) class of universality. A “fruit fly” model of the BKT transition is the classical two-dimensional XY-model on a square lattice, defined by = J (SxSx + SySy). (1) H − i j i j i,j hXi The sum runs over the nearest neighbors, J stands for α the exchange coupling constant and Si stands for the component α = (x,y,z) of the ith spin. We obtained the Fisher’s zeros map via recent Monte Carlo simulations techniques (Replica Exchange Wang- Landau) capable of sampling the entire configuration space efficiently in a single simulation and powerful ma- trix diagonalization procedures. We found that in a BKT transition the internal border of the zeros map behave in such a way that for T TBKT it coalesces into the real positive axis in the thermody-≤ namic limit, indicating the existence of a line of critical points in this region, as should be expected, and in con- trast to what happens for a continuous or discontinuous phase transition, where a single leading zero touches the ENFE - 02/11/2015 - Abstracts 27 positive real axis. This behavior is therefore the signa- important unsolved problems in mathematics. We do not ture of the BKT transition. The inflection point of the aim to provide rigorous results, but we do propose a new zeros map was successfully used to obtain the BKT tem- perspective into this problem, from a physicist point of perature, TBKT =0.704(3), in excellent accordance with view. More specifically, the central limit theorem im- the literature. plies the typical O(√N) bound for the growth of these This work was partially supported by Fapemig. trigonometric series. From this we can argue that the Euler product is still valid inside the right-half part of [02/11/2015 - 17:40 - Room Tubar˜ao] Competing nematic interactions in the XY model the so-called critical strip, thus eliminating zeros in such in two and three dimensions, Gabriel Canova, a region. Yan Levin, Jeferson J. Arenzon, UFRGS Although there is no long-range order at finite SOFT MATTER temperature in two-dimensional systems with continuous symmetry, it is well known that the 2d XY model exhi- [02/11/2015 - 17:05 - Room Vit´oria] bits an unusual infinite order phase transition, associated Combining Statistical Physics and Quantum Me- with integer-vortex unbinding, which belongs to the chanics for Studying Atomic and Molecular Sys- Kosterlitz-Thouless (KT) universality class. In Ref. [1], tems along the Phase Diagram., Sylvio Canuto, a generalization of the XY model with a mixture of IF USP The combination of quantum and statistical ferromagnetic and nematic-like interactions was studied: mechanics allows inclusion of the thermodynamic condi- tion and hence studying atomic and molecular systems H= [∆ cos(θ θ )+(1 ∆) cos(qθ qθ )], in different locations of the phase diagram. In recent − i − j − i − j ij years the studies in the liquid phase have advanced Xh i the knowledge of spectral properties of molecules in with 0 ∆ 1. While the first term favors parallel solution, a situation that is germane in Chemistry and alignment≥ of the≤ spins, the second one tends to induce a of enormous importance in Biology [1]. More recently, 2kπ/q relative orientation between them (k q). The our attention has been devoted to the condition of higher order harmonics (in particular, q = 3 and≤ 8) lead supercritical fluids analyzing the structure, spectra and to further ordered phases and complex phase diagrams. properties of molecules in a supercritical environment, Using a combination of extensive Monte Carlo simulati- [2,3] thus beyond the critical point. Theoretical studies ons, finite size scaling and by studying the helicity mo- of the critical behavior of fluids have been conducted dulus we extend the results of Refs. [1,2] and study the mostly by universal scaling functions and renormaliza- three dimensional case as well. In particular, for q = 8, tion theories. We now focus on the electronic properties the usual ferromagnetic phase is divided in two new pha- of homogeneous fluids close to the critical point and have ses with different kinds of ferromagnetic alignment and given the first explicitly calculated values of the dielectric topological defects. The transitions between the ordered constant in the close vicinity of the critical point (T = phases belong to a wide variety of classes, ranging from Tc + 2K). Thus, the behavior of the dielectric constant, Ising 2D, Kosterlitz-Thouless and an unusual set of criti- only slightly above the critical point, is determined using cal exponents. The results seem to be consistent in three first-principle quantum mechanical calculations. The dimensions, but the transitions between ordered phases multi-scale results [4] obtained by combining statistical with the paramagnetic one are second order and belong and quantum mechanics indicate that the dielectric to the 3D XY universality class. constant of Ar slightly above Tc and around the critical [1] Poderoso, Arenzon and Levin, Phys. Rev. Lett. 106 isochoric (0.531 g/cm3) becomes density-independent. (2011) 067202 Further aspects can be explored and our progress will be [2] Canova, Levin and Arenzon, Phys. Rev. E, 89 (2014) reported in this presentation. 012126 [02/11/2015 - 17:55 - Room Tubar˜ao] References Central Limit Theorems for Trigonometric Se- ries Involving Primes, Guilherme Franc¸a, [1] S. Canuto, Ed., Solvation Effects on Molecules and IFT/UNESP One of the most fundamental results in Biomolecules. Computational Methods and Applicati- probability theory is the central limit theorem, which is ons. Springer (2008). also at the heart of statistical mechanics. Roughly spea- [2] B. J. C. Cabral, R. Rivelino, K. Coutinho and S. king it asserts that a sum of independent random varia- Canuto, J. Chem. Phys. 142, 024504 (2015). bles is normally distributed. We discuss how the central [3] T. L. Fonseca, H. C. Georg, K. Coutinho and S. limit theorem applies to some trigonometric series invol- Canuto J. Phys. Chem. A 113, 5112 (2009). ving the prime numbers. Although the primes are deter- [4] M. Hidalgo, K. Coutinho and S. Canuto, Phys. Rev. ministic, each term in the series behave like independent E. 91, 032115 (2015). random variables due to the multiplicative independence of the primes. Some of these results can be rigorously pro- [02/11/2015 - 17:25 - Room Vit´oria] ven, while others are still conjectural. We discuss these Critical Adsorption of Polyelectrolytes onto Char- trigonometric series in relation to the Zeta function, Di- ged Janus Nanospheres, Sidney J. de Carvalho, richlet L-functions, and also level one modular forms. In Institute of Biosciences, Letters and Exact Sciences the last case there is a close relation with the Sato-Tate - UNESP - Brazil, Ralf Metzler, Andrey G. conjecture. The motivation behind this study is its rela- Cherstvy, Institute for Physics and Astronomy - Uni- tion to the Riemann Hypothesis, which is one of the most versity of Potsdam - Germany Based on extensive Me- 28 Abstracts - ENFE - 03/11/2015 tropolis Monte Carlo computer simulations and analyti- by the polymer energy. Concomitantly, we also study cal considerations we study the electrostatically driven the Arrhenius behavior of the diffusion process at various adsorption of flexible polyelectrolyte chains onto charged temperatures. Finally, we also study the size dependence Janus nanospheres. These net-neutral colloids are com- of the diffusion constant and discuss the implications of a posed of two equally but oppositely charged hemisphe- finite lifetime of polymers of different sizes on a substrate. res. The critical binding conditions for polyelectrolyte [02/11/2015 - 17:55 - Room Vit´oria] chains are analysed as function of the radius of the Ja- Polydispersed rods on the square lattice, nus particle and its surface charge density, as well as the Jurgen¨ F. Stilck, Instituto de F´ısica, UFF and INCT- salt concentration in the ambient solution. Specifically SC, Niter´oi, RJ, R. Rajesh, Institute of Mathematical for the adsorption of finite-length polyelectrolyte chains Sciences, C.I.T. Campus, Taramani, Chennai 600113, onto Janus nanoparticles, we demonstrate that the criti- India We study the grand-canonical solution of a sys- cal adsorption conditions drastically differ when the size tem of hard polydispersed rods placed on the square lat- of the Janus particle or the screening length of the elec- tice using transfer matrix and finite size scaling calcula- trolyte are varied. We compare the scaling laws obtained tions. Only excluded volume interactions are considered. for the adsorption-desorption threshold to the known re- In order to treat both directions on the square lattice in sults for uniformly charged spherical particles, observing a simmetric way, the transfer matrix is defined along the significant disparities. We discovered that there exists no diagonal direction of the lattice. The polydispersity of universal parameter κa, where κ is the reciprocal Debye the rods is determined by distinct activities for internal screening length and a is the nanoparticle radius, that and endpoint monomers of a rod, as is done in a lattice couples the surface curvature and the salinity of the solu- model for equilibrium polymerization. We determine the tion, in contrast to the case for adsorption onto uniformly critical line separating an isotropic from a nematic phase, charged spherical and cylindrical interfaces. We also con- extrapolating data for the correlation length of the model trast the changes to the polyelectrolyte chain conforma- defined on strips of finite width with periodic boundary tions close to the surface of the Janus nanoparticles as conditions. In the full packing limit it was possible to compared to those for simple spherical particles. Finally, handle strips of larger widths, and therefore more pre- we discuss experimentally relevant physico-chemical sys- cise estimates could be obtained. No second transition tems for which our simulations results may become im- to a disordered phase is found at high density, contrary portant. In particular, we observe similar trends with to what is observed in the monodispersed case, therefore polyelectrolyte complexation with oppositely but hetero- the critical line extends up to the full packing limit. The geneously charged proteins. estimates of critical exponents and the central charge, on [02/11/2015 - 17:40 - Room Vit´oria] the whole critical line, and also in the full packing limit, Effects of Monomer Size on Polymer Mass are consistent with the Ising universality class. The ex- Transport at an Interface, Antonio Cadilhe, trapolated phase diagram is compared with Bethe lattice B. V. Costa, Universidade Federal de Minas Gerais results for the same model and with simulational results for monodispersed rods on the square lattice. Polymer mass transport in the bulk has been a topic widely studied in the literature with the main phenome- logical aspects, presently, well understood. These studies are, in general, of great importance to the understanding of the phenomenology of, for example, polymers solutions and polymer melts in the bulk. However, polymer diffu- sion at an interface, as for example, a crystalline subs- trate has been a much less researched topic [Desai et al., Phys. Rev. Lett. 98, 218301 (2007)]. Present studies have focused on smooth surfaces defined by a potential field, which are unrealistic for actual substrates as their structure is not taken into account. In fact, we expect monomer diffusion to take place by thermally activated processes over a corrugated energy landscape, instead of moves over a smooth potential. Here, we study the effect of the substrate structure on the diffusion constant of the polymer, by taking into account its crystalline structure, an FCC (100) substrate orientation. Specifically, we vary the monomer radius relatively to that of the substrate particles and study how the diffusion constant varies. We show that the influence of the substrate is important and leads to a non-monotonic diffusion constant with the ra- tio of the monomer radius relatively to that of substrate particles. This behavior is primarily identified with the total energy, consisting of the polymer energy and the substrate-monomer interaction. The major contribution, leading to the non-monotonic behavior of the diffusion constant, is associated with the substrate-monomer inte- raction, but there is also, a monotonic dependence, given ENFE - 03/11/2015 - Abstracts 29 Plenary talks (8:30 - 10:00) range-interacting many-body classical systems (XY ro- tators and Fermi-Pasta-Ulam-like models), overdamped motion of repulsively interacting vortices in type-II super- PLENARY SESSION conductors, high energy physics (for example distributi- ons of momenta in high energy collisions at CERN/LHC, [03/11/2015 - 08:30 - Room Vit´oria] Brookhaven/RHIC), granular matter (position fluctua- Synchronization and antisynchronization of cou- tions in two-dimensional shear motion), plasma physics pled discrete noisy oscillators, Daniel Escaff, (e.g., distribution of velocities), financial laws (e.g., dis- Kevin Wood, Katja Lindenberg (University of Califor- tribution of price returns and of interoccurrence times), nia San Diego) Synchronization phenomena are observed geophysics (seismic analysis of geological areas in Gre- in many noisy systems in nature. In these systems, a large ece and elsewhere), biology (chemical distances between or infinite collection of units, when coupled together, can classes of nucleotides in DNA sequences of modern and undergo a transition to synchronized behavior in spite of archaic bacteria and Homo Sapiens), cold atoms, image the presence of noise. The theoretical analysis of these and signal processing, among others. A bibliography is phenomena is notoriously difficult, and the numerical si- available at http://tsallis.cat.cbpf.br/biblio.htm mulations notoriously resource intensive. Our work deals with arrays of the simplest possible cou- pled noisy units that exhibit synchronization. Our hope is two-fold: (1) That analytic work is then possible and numerical work much less costly; (2) That the behavior of these “simplest” arrays tells us something about the behavior of more complex realistic systems. Synchronization occurs when the coupled units “like” to be in the same state. Antisynchronization (a term we coined) is a far more complex behavior when the units “do not like” to be in the same state. We present a number of results in this latter case, one that we have not seen discussed in the literature prior to our work. [03/11/2015 - 09:00 - Room Vit´oria] Thermodynamic constraints on information pro- cessing in living systems, Luca Peliti, Institute for Advanced Study, Princeton NJ Life can be understood as a non-equilibrium process driven by information han- dling. It is therefore of great importance to understand the constraints that thermodynamics imposes on the effi- ciency of information processing in a noisy environment. Recent progress in tackling this problem has been made by the use of generalizations of the second law to take into account information, within the general scheme of stochastic thermodynamics. This allows to derive a ge- neral lower bound for error correction that generally re- lates it with dissipation. I shall review these recent deve- lopments and illustrate the results by an application to kinetic proofreading, discussing the corresponding speed- dissipation-accuracy trade-offs. [03/11/2015 - 09:30 - Room Vit´oria] Nonadditive entropies and nonextensive sta- tistical mechanics - An updated overview, Constantino Tsallis, Centro Brasileiro de Pesquisas F´ısicas / Santa Fe Institute Boltzmann-Gibbs entropy and statistical mechanics is one of the pillars of con- temporary physics. It applies extremely successfully to the so called simple systems, whose dynamics is essenti- ally ergodic. When we wish to study complex systems, particularly nonergodic ones, a more powerful theory is needed. For a wide class of such complex systems, no- nadditive entropies and the associated statistical mecha- nics are being currently used and studied. Recent as- pects related to its foundations and applications are now available. A brief overview will be presented. Foundati- ons concerns nonlinear dynamics, large deviation theory, probabilistic correlations, calculation of the index q from first principles, among others. Applications concern long- 30 Abstracts - ENFE - 03/11/2015 Posters (10:00-11:00 / 16:05-17:05) mutator genes are directly selected or not. Our model consists initially of L wild genes which can become beneficial with a selective advantage s, and by a genic BIOLOGICAL PHYSICS favorable mutation rate r, a constant depletion of the population of a lineage that represents the genomic [03/11/2015 - P001] deleterious mutation rate d, and a single mutator gene Optimization on the onset of a criti- that sets the multiplicative factor m to all mutation rates cal phase transition in the visual cortex, of the strain. We show and discuss here analytical and Mauricio Girardi-Schappo, Germano S. Bor- numerical results for the distribution of the ensemble tolotto, Jheniffer J. Gonsalves, Marcelo H. and for the fitness of the ensemble over time, paralleling R. Tragtenberg, Dept. de F´ısica, UFSC, SC, Brasil, them from the distinct scenarios, assessing the effect Leonel T. Pinto, Dept. Eng. Qmc., UFSC, SC, of the different parameters over the evolution of the Brasil Activity in the brain propagates as waves of ensembles, and comparing the latter with data from a firing neurons, namely avalanches. These waves size long term evolution experiment. This work is supported and duration distributions have been experimentally by CAPES, CNPq, and FAPEMIG. shown to display a stable power law profile and to have [03/11/2015 - P003] long-range correlations and 1/f β power spectrum in Normal and tumoral melanocytes exhibit q- vivo and in vitro. These are typical features of critical Gaussian random search patterns, Priscila C. systems. Criticality have the advantages of maximizing A. da Silva, Tiago V. Rosembach, Marcio´ S. Ro- the response dynamic range of neural networks, optimi- cha, Marcelo L. Martins, Departamento de F´ısica, zing memory and learning processes, the computational Universidade Federal de Vi¸cosa, MG, Brasil, Anesia´ A. power of the brain and information processing flexibility. Santos, Departamento de Biologia Geral, Universidade We study a feedforward layered network model of the Federal de Vi¸cosa, MG, Brasil In multicellular orga- primary visual cortex that process input information via nisms, cell motility is central in all morphogenetic pro- avalanches that emerge spontaneously from a constant cesses, tissue maintenance, wound healing and immune input presented to the retina. We show for the first time surveillance, and failures in its regulation potentiates nu- that there is a minimum value for the time that the merous diseases, particularly cancer metastasis. Here, network takes to process input information by varying cell migration assays on plastic 2D surfaces were per- the excitatory postsynaptic potential parameter (EPSP) formed using normal (Melan A) and tumoral (B16F10) close to a critical point. Surprisingly, this point lies murine melanocytes in random motility conditions, i.e., on the edge of a Griffiths phase where avalanches are in the absence of any external gradient of chemotactic power-law distributed and have a 1/f β power spectrum signal. The trajectories of the centroids of the cell peri- with 0.3 β 1.5, matching experiments. The meters were tracked through time-lapse microscopy. The ≤ ≤ order-disorder continuous phase transition point may be statistics of these trajectories was analyzed by building analytically approximated by a mean field calculation, velocity and turn angle distributions, as well as velocity and is located close to the expected experimental value autocorrelations and the scaling of mean-squared displa- of EPSP in the cortex ( 1mV). The system presents cements. We find that these cells exhibit a crossover from ≈ two second order phase transitions which are described a normal to a super-diffusive motion with non-Gaussian by two independent order parameters similarly to the velocity distributions, q-exponentially velocity autocor- Blume-Emery-Griffiths model. We discuss how the relations, and trajectories without angular persistence at model could be extended in order to describe recent long time scales. Furthermore, our results reveal that experimental results of a stable critical point in the B16F10 cells infected by mycoplasmas exhibits essenti- visual system of turtles. ally the same diffusivity than their healthy counterparts. [03/11/2015 - P002] Also, varying the initial density of plated cells, we find Evolution of an ensemble of mutator strains that there is a crossover from anomalous (q > 1) to nor- towards an equilibrium mutation rate, mal (q = 1, Gaussian) migration regime as this density Alexandre de Aquino Soares, UFMG, Louis increases. Finally, a q-Gaussian random walk model was Bernard Klaczko, UNICAMP, Ronald Dickman, proposed to account for these cell search patterns. Simu- National Institute of Science and Technology for Com- lations based on this model correctly describes the cros- plex Systems, UFMG Mutation rates are fundamental sover to super-diffusivity in the cell migration tracks. parameters for evolutionary processes in general. If This work was partially supported by FAPEMIG. they are excessively low, populations may not adapt [03/11/2015 - P004] fast enough to environmental changes and go extinct. Cell aggregation in monolayer culture: clues to If they are excessively fast, deleterious mutations may a universal kinetics, Priscila C. A. da Silva, reach levels unbearable to life as well. Thus, equilibrium Marcelo L. Martins, Departamento de F´ısica, Uni- mutation rates commonly found in nature must be versidade Federal de Vi¸cosa, Vi¸cosa, MG, Brazil, Anesia´ compatible with the very existence of the populations A. Santos, Departamento de Biologia Geral, Universi- they are measured in. Based on a though experiment dade Federal de Vi¸cosa, MG, Brazil, Sidiney G. Al- by Fisher, we investigate the establishment of an equi- ves, Departamento de F´ısica, Universidade Federal de librium mutation rate reached after competition within S˜ao Jo˜ao Del Rei, Ouro Branco, MG, Brasil Cell ag- an ensemble of asexual lineages that differ only by a gregation is a dynamic and complex process ubiquitous in mutator gene which regulate genomic mutation rates life. It occurs in morphogenesis, from organisms situated in scenarios such as under adaptation or not, and if at the border between single and multicellular life forms, ENFE - 03/11/2015 - Abstracts 31 for instance Dyctyostelium discoideum , to mammals in pid bilayers are an excellent experimental model to test which tissues are formed by the assembly of migratory this hypothesis because mimics essential aspects of bio- and similar cells into cohesive groups. Also, aggregation membranes, and gramicidin, whose β-helices dimerize to disorders are present in numerous diseases. The aggrega- form a channel, is a good in situ molecular sensor to esti- tion of animal cells in culture comprises a series of moti- mate the variations in Gibbs energy of deformation. The lity, collision and adhesion processes of basic relevance for transition between conductance states ’open’ and ’clo- tissue engineering, bioseparations, oncology research and sed’ corresponds to the transition between the configura- in vitro drug testing. In the present work, we characterize tions ’dimeric’ and ’monomeric’ of the protein, respecti- the aggregation kinetics of normal and cancer cells in cul- vely, with the equilibrium distribution between the two ture by determining their cluster size distribution functi- conformations given by Boltzmann distribution. Its ope- ons. Our experiments reveal that the complementary cu- ration can be studied with a single molecule resolution mulative distributions for eight cell lines from epithelial using electrophysiological methods. This work charac- and mesenchymal origins are described by stretched expo- terized, through electrical measurements of capacitance nential functions. Also, we find that as time evolves and and conductance, the ion channel activity of gramicidin the cell density increases, a dynamical phase transition under the modulatory effect of anandamide partitioned occurs from an aggregation regime described by monoto- in membranes composed of lipids with fatty acid chain of nically decreasing cluster size distributions to another one different lengths. The endocannabinoid does not change in which these distributions are nonmonotonic, exhibiting the capacitance of the membrane or the amplitude of the local maxima at large cluster sizes. Subtly, the univer- current through the single channel, but produces increase sality of the stretched exponential distributions admits in the frequency of occurrence and the average lifetime distinct cluster growth processes controlled by motility of the open state of the channels. The analysis indicates and adhesion traits of the cells. Finally, both analytical that anandamide exerts a local action without specific calculations based on a Smoluchowski-like mean-field ap- binding to the protein, by altering the elastic properties proach and simulations of an agent based model of the of the bilayer surrounding the channel, thus modulating cell aggregation process were developed in order to des- the hydrophobic coupling membrane/protein and deter- cribe the experimentally obtained cluster size distributi- mining its effects on the operation of the ion channel. ons functions. [03/11/2015 - P006] This work was partially supported by FAPEMIG. Dynamical Monte Carlo for non-equilibrium sys- [03/11/2015 - P005] tems with simultaneous events: application for Molecular interaction of anandamide with gra- Tumor Growth, Marco A A da Silva, Flavio´ H micidin ion channel of biomimetics membranes S Costa, USP The usual Dynamical Monte Carlo modulated by adjustments of the bilayer/protein (DMC) method has the assumption that just one event hydrophobic coupling, D. Medeiros1, L. C. may occur, in systems, in the shortest time scale. On the Silva-Gonc¸alves2, A. M. S. Brito2, M. Arcisio- other hand one can find systems in which several events Miranda2, 1Tecnologia em Sistemas Biom´edicos - Fa- occur simultaneously, i.e., where more than one event ta- culdade de Ciˆencias M´edicas da Santa Casa de S˜ao Paulo kes place in the smallest time scale. In this work we study, / Filosofia - Faculdade de S˜ao Bento; 2Biof´ısica - Univer- as an example, the formulation of Dawson and Hillen for sidade Federal de S˜ao Paulo Endocannabinoids are en- the evolution of a tumor system with active and quiescent dogenous molecules lipidic messengers with amphiphilic cells. In this model, an active element generates simulta- character that bind to cell membrane receptors CB1 and neously two individuals in the quiescent state. Mapping CB2 distributed throughout the nervous system, which this model into one-event approach is possible. However, are targets of the active principle of cannabis. The first we develop here, a more comprehensive Markovian DMC endocannabinoid discovered, and best characterized, is theory, which can include, naturally, simultaneous events. N -arachidonoylethanolamine (anandamide). Endocan- Another remarkable feature of the usual one-event appro- nabinoids also exert direct activities, not mediated by any ach is the non-uniform time intervals: an increment de- type of cannabinoid receptor, by modulating the function pends on the rate and the number of elements responsible of ion channels. This can occur by either chemically spe- for each event type. In the regime of low transition rates, cific interactions with determinated sites of these mem- the system spends long time in the same configuration, brane proteins, or by non-specific interactions mediated and the waiting times are estimated in a way to overcome by the bilayer. We hypothesized that the mechanism for this time consumption with a large time step, making the the non-specific receptor-independent action of ananda- algorithm very efficient. However, when the system re- mide involve the adjustment of the membrane/protein hy- aches a small enough (critical) number of elements, the drophobic coupling by varying physical parameters of the waiting times becomes poorly evaluated, leading to ac- lipidic membrane in the region of insertion of the channel. cumulation of biased errors, and consequently, deviating Adjustment process of hydrophobic lengths can affect the system from its actual trajectory. We will address the conformational state and hence the conductance of this issue here and solve it by rescaling the system size. the ion channel, involving energy cost, the bilayer Gibbs Also, we will extend this approach to cases in which the energy of deformation, which can be analyzed using con- systems are too large to simulate. tinuous theories of elastic deformation of bilayers. This [03/11/2015 - P007] approach abstract up the molecular details of the bilayer, L´evy flights and self-similar exploratory behavi- considering it behaving like a macrostructure presenting our of termite workers, Leticia Ribeiro Paiva, collective mechanical properties well defined as thickness, Universidade Federal de S˜ao Jo˜ao Del-Rei, Octavio intrinsic curvature and modulus of elasticity. Planar li- Miramontes, Sirio Orozco, Universidad Nacional 32 Abstracts - ENFE - 03/11/2015 Aut´onoma de M´exico, Og DeSouza, Alessandra Ma- of dengue cases. We obtain analitically the expressions rins, Universidade Federal de Vi¸cosa It has been es- of global R0 and R0 for each age range [2] and calcu- tablished recently that a variety of animals move and late their values for those epidemics. According to these explore their surroundings in an optimal way following previous scenarios, we conclude that the best strategy to L`evy-like patterns in the statistics of the distances trave- reduce the global R0 of Fortaleza, Goiˆania and Manaus led. Here we analyze exploratory spatial behaviour in iso- is to vaccinate children who are 1 to 9 years old. For Rio lated termite workers kept in large containers, free from de Janeiro it is better to vaccinate people of 2 age ranges: the constrained movements they experience within tun- children who are 1 to 9 years old and children and tee- nels. In this way we were able to assess individual free nagers who are 10 to 19 years old. If the vaccine efficacy exploratory behaviour in clueless environments and away is about 60.8%, we obtain that it is enough to innocu- from social interactions. We show by analyzing over half late 3%, 4% and 4% per week of children who are 1 to 9 a million movement displacements that isolated termite years old in Fortaleza, Goiˆania and Manaus respectively. workers actually exhibit a range of very interesting dyna- In Rio de Janeiro 1% per week of people who are 1 to mical properties –including L`evy flights– in their explora- 19 years old would have to be vaccinated. Furthermore, tory behaviour. Our study analyses anomalous diffusion we intend to find the minimal proportion of vaccinated and structure functions to estimate values of the scaling people necessary to avoid epidemics, assuming a vaccina- exponents describing displacement statistics. tion campaign instead of continuous vaccination. Finally We evince the fractal nature of the movement patterns it would be interesting to extend that analysis to other and show how the scaling exponents describing termite cities as well as to analyse the effective reproduction num- space exploration intriguingly comply with mathematical ber. relations found in the physics of transport phenomena. [1] Tasman H, Supriatna AK, Nuraini N, Soewono E. A By doing this, we rescue a rich variety of physical Dengue Vaccination Model for Immigrants in a Two-Age- and biological phenomenology that can be potentially Class Population. Int. J. Math. Mathl. Sci., 2012: 1-15, important and meaningful for the study of complex 2012. animal behavior and, in particular, for the study of how [2] Van den Driessche P, Watmough J. Reproduction patterns of exploratory behaviour of individual social numbers and sub-threshold endemic equilibria for com- insects may impact not only their feeding demands partmental models of disease transmission. Math. Biosci. but also nestmate encounter patterns and, hence, their 180: 29-48, 2002. dynamics at the social scale. [03/11/2015 - P009] Diffusion of hard spheres a binary quenched- Reference annealed mixtures, T. P. O. Nogueira, Instituto Miramontes O, DeSouza O, Paiva LR, Marins A, Orozco de Ciˆencias Exatas, Departamento de F´ısica, Universi- S (2014). L`evy Flights and Self-Similar Exploratory dade Federal do Amazonas - UFAM, Av. Gen. Ro- Behaviour of Termite Workers: Beyond Model Fitting. drigo Ot´avio Jord˜ao Ramos, 3000, Coroado, Campus PLoS ONE 9(10): e111183. Universit´ario, Setor Norte, CEP 69.077-00, F. Pi- azza, Universit´ed’Orl´eans, UFR Facult´edes Sciences, Acknowledgements D´epartement de Physique et Sciences de L’Ingenieur La- We thank the Brazilian Ciˆencia Sem Fronteiras program boratoire: CBM-CNRS UPR 4301 du CNRS, Rue Char- (CSF-CAPES) 0148/2012 and Fapemig for funding. les Sadron, 45071 Orl´eans CEDEX 2 FRANCE. In [03/11/2015 - P008] quenched-annealed (QA) mixtures of hard spheres (HS), Analysis of dengue vaccine through an age- a given fraction of the particles is mobile (volume fraction structured model using actual epidemics data, φm), while the rest are fixed and act as obstacles (volume Luciana Cardim, Maria da Conceic¸ao˜ Costa, Ma- fraction φo). Typically, the phase diagram of QA mix- ria da Gloria´ Teixeira, Instituto de Sa´ude Cole- tures in the (φm, φo) plane features a region where the tiva - UFBA, Rodrigo Carvalho, Instituto de Ma- mobile particles are diffusive, separated from a localized tem´atica - UFBA, Suani Pinho, Instituto de F´ısica - phase by the void percolation line, where the diffusion UFBA Many efforts have been done in the last years for becomes anomalous. the development of a tetravalent vaccine against dengue. In this work, we have investigated the self-diffusion coef- It is expected that, at the very beginning of vaccination ficient of mobile HSs in binary QA mixtures for different campaigns, there won’t be enough vaccines for the whole values of the ratio α between the diameter of the mobile population. Therefore, mathematical modelling is a very HSs and that of the obstacles. We find that the mo- important tool to exhibit different scenarios concerning tion is always diffusive, with a diffusion coefficient that the most efficient strategy to avoid epidemics, i.e., to re- decreases linearly with increasing values of α. For large duce the basic reproductive number R0 below unit. In volume fraction of the obstacles we find a more complex this work, inspired by the literature[1], we propose a mo- decrease, that can be approximated with two successive del with age structure for human compartments (1-9, 10- linear trends with different slopes. In the α 0 limit we 19, 20-29, 30-39, 40-49, 50-59, over 60) and homogeneous recover the well-known mean-field result. Furthermore,→ for vector compartiments, assuming continuous vaccina- we show that in the limit α 1 the diffusion coefficient tion. The infection rate values are based on the force of of monodisperse QA mixtures→ as a function of the obs- infection for different age ranges of actual epidemics oc- tacle packing fraction behaves as an order parameter for curred in some Brazilian cities: Fortaleza (2008), Goiˆania the mobile-to-localized transition, allowing one to recover (2010), Manaus (2011), and Rio de Janeiro (2008). The the void percolation threshold at the same value of φo as chosen epidemics presents, for each city, the highest peak predicted by mode-coupling theory. ENFE - 03/11/2015 - Abstracts 33 COMPLEXITY & INTERDISCIPLI- lity. We determine several critical values for p, q and w, NARY TOPICS which separate an ordered phase (where the majority of the agents presents positive or negative opinion) from a [03/11/2015 - P010] disordered phase (where several opinions coexist in the Simulations of Segregation and Ripples on Un- population). The critical exponents for such transitions paved Roads, Tiago Moy da Silva, Americo´ suggest that the inclusion of these new parameters does Tristao˜ Bernardes, Programa de P´os-gradua¸c˜ao em not change the universality of the model, i.e, the model Ciˆencia - F´ısica de Materiais, Depto de F´ısica, Univer- also belongs to the mean-field Ising model universality sidade Federal de Ouro Preto In this work we present class. In addition, we compare histograms of the opini- a study on the ripples formation in unpaved roads. This ons in the society for distinct values of the parameters, for effect, also known as washboard road, annoys thousands the model with and without conviction. In this case, it is of people around the world and it does not exist yet a possible to see that inclusion of the convictions strongly closed theory about it. This study is made with Mole- decreases the fraction of extremist agents in the popu- cular Dynamics Simulation applied in soft grains in two lation, whereas the fraction of moderate and undecided dimensions. In this model, the grains are 2d disks with agents increases, making the model more realistic. motion of translation and rotation and under action of [1] S. Biswas, A. Chatterjee, P. Sen, Physica A 391 (2012) a constant gravitational field. The simulations are per- 3257-3265. formed in a box with horizontally periodic boundaries. [2] Nuno Crokidakis, Phys. Lett. A 378 (2014) 1683- The force of contact has a radial component, also cal- 1686. led spring dashpot model, and a tangential component, which charges the friction between the grains. Simula- [03/11/2015 - P012] ting a rolling wheel, a large grain rolls over the other A self regulated adaptive model for expendi- small disks. In the simulations we observed that the rip- ture propensity and Gini index relationship, ples can arise or not together with the segregation of the Alan de Andrade Santos, Pedro Hugo de Fi- grains, but recent articles showed that this phenomenon gueiredo,ˆ DF - UFRPE - PE - Brasil Over the past is not determinative to the formation of the corrugations, two decades, physicists have been devoted to the problem although they are observed in the real roads. We inves- of income distribution P (m). A key feature in this study tigate the evolution of the ripples through of fast Fourier is characterize the inequalities implied by microeconomic transform (FFT) and we analyzed the segregation by ra- models based on the mechanisms of exchange of goods dial distribution function (RDF). We also verified some and services. One way to quantify such inequalities is ba- cases by changing the basic model parameters: physical sed on the Gini index 0 6 G 6 1, a parameter that sets quantities and geometric elements which play some role the maximum (G = 1) and minimum (G = 0) concentra- in this problem. tion of resources. Current studies indicates that income Acknowledgment: UFOP, CNPQ, CAPES and FAPE- distribution P (m) has two distinct regimes separated by a MIG scale mc. The first one associated to a low-regime income (m m ) described by a gamma distribution Γ(n,β) and [03/11/2015 - P011] 6 c Effects of noise and conviction in kinetic mo- a second one related to a high-income regime (m>mc), dels of opinion dynamics with continuous states, mathematically represented by a power law function with A. R. Vieira, N. Crokidakis, Instituto de F´ısica, Uni- a parameter 1 6 ν 6 2, usually called Pareto’s exponent. More recently it has been pointed out the existence of a versidade Federal Fluminense, Niter´oi/RJ, Brazil In this work we study a kinetic exchange opinion model ba- bimodality on this distribution. In close connection with sed on [1,2], where the individuals (agents) in an artificial microscopic models usually constructed to describe phy- society present continuous opinions in the range [-1.0,1.0]. sical systems, two classes of models were introduced as a For a given interaction, we randomly chose 2 agents i and intent to mimic a closed economic system, compound by j, which characterizes a mean-field-like approach. The a fixed number of economic agents N and resources M. opinion of the agent i at the time t + 1 is updated fol- At the first class (homogeneous) which describes the low- lowing the rule regime income, agents have the same consumption ex- penditure ω (0 < ω 6 1), at the second (heterogeneous) oi(t +1)= cioi(t)+ µij oj (t), providing a power law there is a single consumption ex- penditure ωi, specific to each agent, or in a more realistic where the interaction between i and j (µij ) is positive or case a probabilistic distribution S(ω). In both cases the negative, according to a parameter p. We also consider expenditure consumption rate are set exogenously to the that each agent has a conviction about his opinion, a system. In this communication we introduce an adaptive real number that can be either positive or negative. On heterogeneous model in order to describe quantitatively the other hand, we consider the independent behavior of the relationship among the average expenditure rate ω the agents, i.e., with a probability q the agent i changes of economic agents, and the Gini index associated toh thei his opinion independently of the interactions with other income distribution. In this approach a fraction p0 of all individuals. economic agents N do not modify their expenditure ra- We studied the model via computer simulations. We in- tes, a fraction p1 are able to modify their consumption vestigate numerically the evolution of the opinions in the rate negatively correlated with their income and lastly a society, and we verify that the system reaches stationary fraction p2 positively. In this scenario the inertia γ(m) states. We studied some quantities of interest, for exam- associated with adaptation is self-regulated by the agent ple the “magnetization”of the system, the fourth-order income level. Besides producing the distribution rates as cumulant and an analogous of the magnetic susceptibi- an emerging feature the model are able to provide a bi- 34 Abstracts - ENFE - 03/11/2015 modality on the income distribution and produce values depends on a hyperparameter that estimates the trust of ( ω , G) compatible with those available from real data one agent on the information provided by the other. If obtainedh i from the World Bank. the expected value of the total cost function is relevant [03/11/2015 - P013] information, Maximum Entropy permits characterizing Competition between collective and individual the state of the society. Furthermore we introduce a dy- dynamics: Applications to simple economic mo- namics on the trust parameters, which increases when dels, Diego F. de Almeida, Andre´ P. Vieira, Uni- agents concur and decreases otherwise. We study the re- versidade de S˜ao Paulo Using Grauwins generaliza- sulting phase diagram in the case of large number of in- tion [1] of Schelling’s segregation model [2] we study, teracting agents on a complete social graph, hence under in a simplified model, some consequences of the ”fiscal sympatric conditions. Simulations show that there is evo- war”waged between the states of a federation, and of the lution of assortative distrust in rich cultural environments “rate tax”generated by the recent Brazilian Central Bank measured by the diversity of the set of issues under dis- regulation of bank credit portability. The system is di- cussions. High distrust leads to antilearning which leads vided into blocks and all blocks have the same utility to multiple groups which hold different opinions on the function, which measures the satisfaction of agents living set of issues. We simulate conditions of political pressure there and depends on the density of agents. We introduce and interaction that describe the House of Congress of a disorder parameter in one of the blocks to make it more Brazil and are able to qualitatively replicate voting pat- attractive than the others, so as to mimick the essential terns through four presidential cycles during the years of igredient of competition between states or banks. 1994 to 2010. In the application to the scenario of a fiscal war between [03/11/2015 - P015] the states of a nation, we interpret blocks as the states The evolution of cooperation in structu- of a federation and economic agents as companies that red populations with influence of nature, make decisions seeking to increase their own satisfaction. Elton J. S. Junior´ , Jafferson. K. L. da Silva, A vacant state, in order to attract agents already esta- Universidade Federal de Minas Gerais, Lucas Wardil, blished elsewhere, need to give more incentives to attract University of British Columbia, Canada Cooperation investment because of its low utility. In this work we try is commonly illustrated as a Prisoner’s Dilemma game. to quantify the costs that states have with this kind of Players obtain 1 (reward) for mutual cooperation and action. b for mutual defection (punishment); in the case in Another analysis of the results can be applied to a bank which they choose different strategies, the cooperator credit portability model, where we interpret economic obtains 0 (sucker) and the defector obtains b > 1 agents as customers and blocks as retail credit banks. (temptation). Although individual self-interest may The interest rate levied on each bank will depend on the not favor cooperation, it can evolve if, for example, size of the portfolio of that bank. Having a bank with players interact multiple times adjusting their behavior a differentiated interest rate makes it more attractive accordingly to opponent’s previous action. In addition than others, and it begins to ”steal”customers from other to, if individuals interact to each other as in a structured banks. Studying the selfish scenario (where the govern- population (in square lattice, for instance), cooperators ment doesnt discourage a client from taking his/her debt can survive by giving origin to clusters; this phenomena to another bank), and assuming that the number of cus- is known as spatial reciprocity. However, it happens tomers in the market is sufficiently small, the dynamics that sometimes a player, even being a cooperator, is not leads to a situation where we have just a few coexisting able to cooperate because of lack of resources (caused by banks, the others having gone bankrupt. nautral disasters, migration, etc.). In this present work We study analytically the effects, at the global level, of we intend to model the role played by nature setting variations in the density, in the altruism parameter and some nodes of the lattice as empty nodes (inactive in the parameter determining the utiliy function at sa- nodes). If an individual is in one of this sites, it is turation, as well as the effects of introducing disorder in not able to do anything once there are no wherewithal one or more blocks. Finally, computer simulations were there, no matter it is either a cooperator or a defector. performed to check that the dynamic behavior in all sce- We studied the fraction of cooperators on stationary narios was consistent with the obtained solutions. state as a function of both w (fraction of active nodes) [1] S. Grauwin et al., PNAS 106, 20622 (2009). and b (tendency of desertion). The authors thank to [2] T. C. Schelling, J. Math. Sociol. 1, 143 (1971). FAPEMIG, CAPES and CNPq for financial support. [03/11/2015 - P014] [03/11/2015 - P016] Sympatric Multiculturalism in Opinion Models, Leaking Quantum Square Billiards, Felippe Alves, Nestor Caticha, Instituto de F´ısica Emanuel Vicente Chimanski, Brett Vern Carl- - Universidade de S˜ao Paulo While social interactions son, Instituto Tecnol´ogico de Aeron´autica, Eduardo tend to decrease differences in opinions, multiplicity of Vicentini, Universidade Estadual do Centro Oeste groups and individual opinion differences persist in hu- Open systems are often applied to model natural phe- man societies. Axelrod identified homophily and social nomena in many branches of physics and are commonly conformity seeking as basic interactions that can lead to related to leaking systems. Problems with leaks also multiculturalism in spatial scenarios in models under cer- play an important role in the framework of dynamical tain special conditions. We follow another route, where theories. Quantum billiards are the quantum version of the social interactions between any two agents is given by two-dimensional classical systems in which the particle the descent along the gradient of a cost function deduced dynamics is restricted by walls. In this work, a closed and from a Bayesian learning formalism. The cost functions an open square quantum billiards are studied. The wave ENFE - 03/11/2015 - Abstracts 35 functions of the problems are obtained by the boundary the set of unrealized highest buy (lowest sell) orders of wall method. Plane waves with different energies are the order book, which comprises the potential next tra- scattered by the infinity potential defined on the billiard ding. In order to explain the non-Gaussian character of table boundary. The influence of the gap size d in a wall market price fluctuations, we consider extensions in the of the open system is studied in comparison with results form of Langevin-type equations with an inertia term. of the closed version of the system. In this investigation The observed financial motion is described as analogous the probability density function is computed for both the to a damped harmonic particle embedded in an environ- open and closed billiards. Prelimenary results, show that ment which depicts the accumulated orders in the un- the presence of a leak shifts the resonant states related derlying optimal levels of the order book. Memory is a to the closed billiard and large values of d can displace crucial ingredient for the collective properties of markets, hight exited states. The flux of probability current is especially in the short time regime, and this is account calculated on the leak and the relation between wave by a non-local exponential kernel in the anticipation of energy and the leaking was studied. In addition the prices by the agents when placing their orders. Using a energy level distribution is calculated and compared to non-Markovian Langevin description, we consider a ran- Poisson and Wigner distributions. dom damped harmonic particle in presence of noise. The noises, which represent external and/or internal pertur- [03/11/2015 - P017] Dynamical Properties of the Kleinberg networks, bations, are modeled as an Ornstein-Uhlembeck process Samuel Morais da Silva, Saulo-Davi Soares e and/or as a dichotomous process which show to be more Reis, Ascanioˆ Dias Araujo, Jose´ Soares de An- amenable to analytic approaches. Indeed, we can picture two subpopulation of trades, buyers and sellers, exchan- drade Jr., Universidade Federal do Cear´a A great number of systems defined as complex consist of inter- ging particles at rate 1/τ via some idiosyncratic switching connected parts or individual components performing a process. We provide the expression for the low order ex- network or graph. Communication between the parts is pansion in τ of the effective damping and restoring pa- essential for their existence so that it is necessary a better rameters, in the case where a dichotomous noise process understanding of their ability to communicate depending is at play. We also analyze the expected values as well on the amount of information that transits. The dyna- as the dispersion of the log price and the returns analyti- mics of package transport in these systems and the emer- cally and numerically. Using random damped harmonic gence of congestion are problems of high scientific and oscillator models as a reference tool, we conclude by in- economic interest. In this work we investigate the dyna- vestigating the intra-day Brazilian stock price series. mical properties of transport of packages (informations) between sources and previously defined destinations, con- COMPLEXITY & INTERDISCIPLI- sidering different models of spatially embbeded networks NARY TOPICS such as lattice and Kleinberg. More precisely, we study a second-order continuous phase transition from a phase [03/11/2015 - P019] of free transport to a congestion phase, when the pac- Effects of mobility in the epidemic threshold kages are accumulated in certain regions of the network. of the SIS dynamics in scale-free networks, By means of a Finite Size Scaling, we describe this phase Diogo da Silva, Costa Ferreira, Universidade transition characterizing its critical exponents. For 1D Federal de Vi¸cosa-MG Many real systems as food and 2D lattice networks, we observe that the critical pa- webs, friendship networks, transportation and scientific rameter pc scales with exponents approximately 1 and collaboration can be suitably described in he framework − 0.5 with respect to the system size. In the case of Klein- of complex networks. The behavior of dynamical − berg newtorks where shortcuts between two nodes i and processes on the top of them is of great interest, being j are added to the network according to a probability the epidemic spreading one of the most important α distibution given by P (rij ) r− , we show that the best issues of the field. The simplest epidemic model is the ∼ ij scenario occurs when α = d, where d is the dimention susceptible-infected-susceptible (SIS), in which every of the topology structure. In this regime, package traffic infected vertex of the network transmits the infection were shown to be more resilient to the increase of num- to each contact at a constant rate λ and becomes spon- ber of packages in the network. The confirmation of our taneously susceptible at an unitary rate. In this work, result is obtained not only from direct measure of order we perform simulations of the SIS including mobility of parameter, that is, the ratio between undelivered and ge- infected individuals on networks with a power-law degree γ nerated packets, but is also supported by our analysis of distribution P (k) k− . The diffusion process consists finite size. in exchanging an infected∼ vertex and one of its neighbors [03/11/2015 - P018] at rate D. The theoretical analysis of the SIS dynamics Non-Markovian models for short-scale financial is done through the degree based mean field (DBMF) motion, Victor Galvao˜ , R. Riera, Department of theory, which assumes that vertices with the same degree Physics, PUC-Rio and National Institute of Science and have the same behavior, and by the individual based Technology for Complex Systems,Rio de Janeiro, Brazil mean field (IBMF) theory, which considers individual The random nature of financial price fluctuations is con- properties of each vertex by means of the adjacency sidered as resulting from the imbalance of buy and sell matrix. These theories predict different outcomes for orders at each time step. In this work, we explore mi- the epidemic threshold for exponents γ < 3 and γ > 3. nimal models of the behavior of the financial agents to Our simulations for γ < 3 exhibit a good agreement study the emergence of short-scale behavior of prices. At with both theories, which are equivalent. For γ > 3, we a given time, the state of the market is characterized by observed a finite epidemic threshold which converges to 36 Abstracts - ENFE - 03/11/2015 the DBMF threshold for large diffusion rate contrasting titles come from 15 scientific journals high-impact. For a with IBMF theory. Multiples transitions are observed given network is also built a time-varying graph (TVG). for small diffusion coefficient but disappear in the large We consider a window bimonthly (week by week) and diffusion limit. We explain this the crossover from a advancement in time shows the evolution of networks of IBMF to a DBMF regime in terms of the lifespan of words from the titles of papers published. The analysis epidemic activity on the hubs of the network. is carried out using indicators timeless. Entropy is calculated based on the uncertainty of edges and vertices We acknowledge Fapemig by the financial support. of each network. The probabilities are associated with overlapping edges and vertices in the formation of the [03/11/2015 - P020] Effect of Spatial Distribution of Traffic Lights to titles network, taking into account the relative frequency the Traffic Flow Behaviour, C. F. M. Magalhaes˜ , of these indicators before clicks are joined. Thus, it becomes possible to compare different journals, as R. A. Cabral, UNIFEI We present some preliminary results of a study that extends the work by D-W Huang well as a same journal at different times (through the and W-N Huang [1]. They proposed a model to describe TVG). The results suggest that these journals can be the traffic from suburb to downtown during the rush grouped, based on their entropy values and indices hours. The model is a cellular automaton which consists of some networks. This study may contribute to the of a 1D open lattice with regularly spaced traffic lights study of communication and scientific collaboration and and parking lots and vehicles that enter the lattice at dissemination of human knowledge. one end and left it at a parking lot or at the other [03/11/2015 - P022] end. The vehicles evolve following the single lane Nagel Optimal Path Cracks in Complex Networks, and Schreckenberg local dynamics [2]. We investigate T. C. Nunes, L. R. da Silva., Departamento de F´ısica how changes in traffic lights spacing affects the traffic Te´orica e Experimental - UFRN, J. S. Andrade, A. A. behaviour. The motivation was the fact that the Nagel Moreira., Universidade Federal do Cear´a As we can and Schreckenberg dynamics exhibits a critical state as see in nature, we are surrounded by materials from which the density of vehicles approaches a determined value [3]. their structures have some kind of disorder that may be In that state, the stream of vehicles self-organizes into a related to microscopic voids, detachments and even struc- fractal structure that reflects a power law distribution of tural composition, which makes them susceptible to frac- jam sizes. The initial results indicate that a power law tures that depend on the degree of disorder significantly distribution of the traffic lights spacing tends to increase wherein the material is given. For this reason optimal the stream flux no matter the value of traffic lights paths play a fundamental role in physical numerous ap- period and the inflow rate. Nevertheless, in contrast plications ranging from random polymers to brittle frac- to the regularly arranged traffic lights model, a power ture, from the flow through porous media to information law distribution spacing caused a high sensitivity of the propagation. Following the study of optimal path cracks stream flux to the inflow rate. (OPC) on regular square lattices, here we investigate the same problem in Complex Networks. In this problem we [1] Huang, D-W.; Huang, W-N. A model for city traffic associate to each site a determined energy. The optimum in rush hours. Chinese Journal of Physics, Taipei, v. 45, path is defined as the one among all possible paths that n. 6-II, p. 708-715, dez. 2007. crosses the system which has the minimum cost, namely the sum of the energies along the path. Once the op- [2] Nagel, K.; Schreckenberg, M. A cellular automaton timum path is determined, at each step, one blocks its model for freeway traffic. Journal de Physique I France, site with highest energy, and then a new optimal path Paris, v. 2, n. 12, p. 2221-2229, dez. 1992. is calculated. This procedure is repeated until there is a set of blocked sites forming a macroscopic fracture which [3] Nagel, K.; Paczuski, M. Emergent traffic jams. connects the opposite sides of the system. As observed in Physical Review E, New York, v. 51, n. 4, p. 2909-2918, the work on regular square lattices, the fractured system abr. 1995. studied here also presents different behaviors depending on the level of disorder, namely weak, moderated and [03/11/2015 - P021] strong disorder intensities. In the regime of weak and Shannon entropy applied in networks moderated disorder, while the density of removed sites in based on titles of scientific papers, the system does not depend of the size L in the case of Marcelo do Vale Cunha, Hernane Borges de regular lattices, in the regime of high disorder the density Barros Pereira, Marcelo Albano Moret Simoes˜ becomes substantially dependent on L. We did the same Gonc¸alves, Programa de Modelagem Computacional, type of study for Complex Networks. In this case, each SENAI Cimatec, Av. Orlando Gomes 1845, 41.650-010, new site is connected with previous ones. As in the pre- Salvador, BA, Brazil Recently, semantic networks vious work, we observe that the density of removed sites based on titles of scientific papers have been explored to presents a similar behavior. Moreover, a new result is study the formal system of scientific communication: the obtained, i.e., we analyze the dependency of the disorder journal. The network theory along with the Shannon with the attachment parameter m. entropy of information can give interesting insights on [03/11/2015 - P023] how to differentiate journals. We present an application Modelling optimism and the spread of false ru- of Shannon entropy in semantic networks based on mours in sociophysics., Andre´ M. Timpanaro, titles of scientific papers. These networks are formed Instituto de F´ısica da Universidade de S˜ao Paulo, Brazil considering the words of a title as vertices of a click. The In the recent years, physicists have given a great deal of ENFE - 03/11/2015 - Abstracts 37 attention to the study of social models using tools from Brazil Theoretical and computational approaches to statistical physics, dubbed sociophysics. The main pur- epidemic-like models have met with outstanding success pose of sociophysics is to use results from experiments on complex networks. However, some questions remains in psychology as a guide to define microscopic rules to opened for the dynamics of the Susceptible-Infected- be used in computational models of different sociological Susceptible (SIS) model on networks with a heavy-tailed and political phenomena. A great variety of such models degree distribution. This archetypal disease spreading exist, so a ”unified language”is desirable for introducing model undergoes an absorbing phase transition revea- modifications. In a previous work we introduced the idea ling its epidemic threshold at some value for the effective of confidence rules [A. M. Timpanaro and C. P. C. do spreading rate. We numerically test the limits and va- Prado, Phys. Rev. E 80, 021119 (2009)] as a framework lidity of two competing theoretical approaches proposed to introduce biases and prejudices in these models. to describe the SIS epidemic threshold on uncorrelated γ In this work we apply the notion of confidence rules to networks with degree distribution P (k) k− . On one the Sznajd and voter models in order to study 2 different hand, we have the Heterogeneous Mean-Field∼ (HMF) ap- situations: proach that assumes the statistical equivalence for those nodes of the same degree class (same number of contacts). Optimistic and pessimistic voters, using a rule with • On the other hand, the Quenched Mean-Field (QMF) four opinion states that are symmetric, but interac- considers the entire connectivity pattern of the network ting in a non-associative way. but treating the state (infected or not) of neighboring Propagation of false rumours, using a rule with th- nodes as being statistically independent. We investigate • ree opinion states, reminiscent of the SIR model. network properties in which analytical results derived un- der the theoretical assumptions of HMF and QMF are or We are able to explain 50-50 splits with alternance of not verified. We show that the presence of outliers and power in the case of the optimism/pessimism model and formation of densely connected cores on these networks we find distinct network signatures in the time series ob- drastically change the outcomes predicted by these the- tained for the rumour spreading model. oretical approaches. Moreover, resorting to extensive si- mulations for a large ensemble of network realizations, we [03/11/2015 - P024] COMPLEX NETWORK ANALYSIS OF show that network samples (for the regime of γ > 3) with BRAZILIAN POWER GRID, Keila Melo, the presence of outliers can produce a diverging average Fabricio L. Forgerini, Federal University of Amazo- lifetime for the model, showing that the epidemic lifetime averaged over the ensemble is infinite even for finite sizes nas Power Grids and other delivery networks has been attracted some attention by the network literature last independently of the infection rate. decades. Despite the Power Grids dynamics has been controlled by computer systems and human operators, the static features of this type of network can be studied The authors would like to thank FAPEMIG. and analyzed. The topology of the Brazilian Power Grid [03/11/2015 - P026] (BPG) was studied in this work. We obtained the spatial From epidemic hotspots to super-spreading structure of the BPG from the ONS (electric system’s events, Ronan S. Ferreira, Instituto de Ciˆencias national operator), consisting of high-voltage transmis- Exatas e Aplicadas, Universidade Federal de Ouro Preto, sion lines, generating stations and substations. The local 35931-008, Brazil, Rui A. da Costa, Department of low-voltage substations and local power delivery as well Physics& I3N, University of Aveiro, 3810-193, Portugal, the dynamic features of the network were neglected. We Sergey N. Dorogovtsev, Department of Physics& analyze the complex network of the BPG and identify I3N, University of Aveiro, 3810-193, Portugal; A. F. the main topological information, such as the mean Ioffe Physico-Technical Institute, 194021, Russia, Jose´ degree, the degree distribution, the network size and F. F. Mendes, Department of Physics& I3N, University the clustering coefficient to caracterize the complex of Aveiro, 3810-193, Portugal We examine the pheno- network. By the network analysis we also detected menon of localization and super-spreading by introducing the critical locations (nodes and links) on the network a superhub of degree q N α on different network to- and, therefore, the more susceptible points to lead to a pologies with N nodes.∼ It provides high heterogeneous cascading failure and even to a blackouts. Due to the and controlled environments by tuning the gap exponent characteristic of the topology and physical structure α. Recently, localization phenomenon attracted much at- of the network, we show that the BPG is not resilient tention to the issue of epidemic spreading on networks, against random failures, when a fraction ρ of the links where this phenomenon means persistence of an island are randomly removed, the network may disintegrates of disease below the epidemic threshold around a stron- into smaller and disconnected parts. We believe that the gly connected node or a dense cluster. This phenome- even a static study of the network topology can help to non hinders the observation of the epidemic threshold identify the critical situations and also prevent failures in complex networks with hubs and heavy-tailed degree and possible blackouts on the network. distributions. The problem is that the SIS (susceptible- [03/11/2015 - P025] infective-susceptible) epidemic model has an absorbing Caveats on epidemic processes model on complex state in which infection is absent, and so below the epi- networks, Ronan S. Ferreira, Instituto de Ciˆencias demic threshold, islands of disease with a finite number Exatas e Aplicadas, Universidade Federal de Ouro Preto, of infective nodes cannot survive forever. In other words, 35931-008, Brazil, Silvio C. Ferreira, Departamento a system with a finite number of infected nodes has a de F´ısica, Universidade Federal de Vi¸cosa, 36570-000, non-zero probability to recover immediately. For a large 38 Abstracts - ENFE - 03/11/2015 but finite number of infected nodes, however, this proba- Ismael V. L. Costa, Fernando A. Oliveira, bility is small, so the complete recovery can take a long Universidade de Bras´ılia - UnB In a recent work [1] time. We show that in the heterogeneous SIS model lo- a method to derive analytically the roughness evolution calization should be only metastable, manifesting itself was exposed. The method allows to obtain analytically in the form of long-lasting local outbreaks of the disease the growths exponents of a surface of 1 + 1 dimensions below the epidemic threshold. Moreover, super-spreading whose dynamics is ruled by cellular automata. The events in which one or a few infective individuals spread method was successfully applied to the etching model a disease providing an unusually large number of second [2,3] and the dynamical exponents where obtained. cases, has great importance on current understanding on Those exponents are exact and they are the same as epidemic spreading. central issue is that heterogeneity in those exhibited by the KPZ model [4] for this dimension. population structures, such as the presence of outliers on We applied the method as well to RSOS model [5,6] and networked systems, accelerates infectious disease spread. we confirm that the very old conjecture that, the RSOS We present under what circumstances the role reversal model and KPZ belong to the same universality class. from a hotspot to a super-spreading event takes over for We show as well a very general procedure to classify the SIS model on heterogeneous networks. the models without hard calculations. This method allows us to verify the universality class of the automata cellular model [7]. RSF would like to thank FAPEMIG. [1] W. S. Alves et al to be published. FUNDAMENTAL ASPECTS OF STA- [2] B. A. Mello, A. S. Chaves, and F. A. Oliveira, Phys. TISTICAL MECHANICS Rev. E 63, 041113 (2001). [3] E. A. Rodrigues, B. A. Mello, and F. A. Oliveira, J. [03/11/2015 - P027] Phys. A 48, 035001 (2015). Real-Space, Mean-Field Algorithm for Calcula- [4] M. Kardar, G. Parisi, and Y. C. Zhang, Phys. Rev. ting Long-Range Dipolar Interactions in Model Lett. 56, 9, 889 (1986). Systems, Antonio Cadilhe, B. V. Costa, Univer- [5] Halpin-Healy T J and Zhang C-Y, Phys. Rep. 254, sidade Federal de Minas Gerais Long-range interacti- 215 (1995). ons are known to be of difficult treatment in statistical [6] Marsili M, Maritan A, Toigo F and Banavar J R, Rev. mechanics models. There are some approaches that in- Mod. Phys. 68, 963 (1996). troduce a cutoff in the interactions or make use of reac- [7] W. R. Julvito et al to be published. tion field. However, those treatments suffer the illness of [03/11/2015 - P029] being of limited use, in particular close to phase transi- JARZYNSKY EQUALITY IN THE POLY- tions. The use of open boundary conditions allows the MER TRANSLOCATION PROBLEM, sum of the long-range interactions over the entire system Nicolau G. Borsato, Taiana F. Cardoso, F. to be done, however, this approach demands a sum over Mondaini, CEFET-RJ Campus Petr´opolis, L. Mori- all degrees of freedom in the system that makes a nume- coni, UFRJ The process of polymer translocation rical treatment prohibitive. Techniques like the Ewald occurs in many biological and biotechnological phe- summation or fast multipole expansion account for the nomena. It has received great attention in both exact interactions but are still limited to a few thousands experimental and theoretical studies in recent years due particles. In this talk we introduce a novel mean-field to its important role in many crucial biological processes, approach to treat long-range interactions. The method such as mRNA translocation across a nuclear pore is based in the division of the system in cells. In the complex, drug delivery, injection of DNA from a virus inner cell, that contains the particle in sight, the ’local’ head into a host cell and gene therapy. However, due to interactions are computed exactly, the ’far’ contributions the complexity of the interactions involved, especially are computed as an average for each of the remaining between the pore and the membrane, computer simula- cells. Using this approach, the large and small cells li- tions have been widely used as a fundamental research mits are exact. At a fixed cell size, the method also beco- tool. Most of the numerical studies can be classified into mes exact in the limit of large lattices. We have applied the topical issues of (i) translocation driven by chemical the procedure to the two-dimensional anisotropic dipolar potential gradients, (ii) translocation driven by external Heisenberg model. A detailed comparison between our forces, and (iii) unbiased translocation. method, the exact calculation and the cutoff radius ap- We perform, with the help of cloud computing resour- proximation were done. Our results show that the cutoff- ces, extensive Langevin simulations, which provide free cell approach outperforms any cutoff radius approach as energy estimates for unbiased three-dimensional polymer it maintains the long-range memory present in these in- translocation. We employ the Jarzynski equality in its ri- teractions, contrary to the cutoff radius approximation. gorous setting, to compute the variation of the free energy Beside that, we calculated the critical temperature and in single monomer translocation events. In our three- the critical behavior of the specific heat of the anisotropic dimensional Langevin simulations, the excluded-volume Heisenberg model using our method. The results are in and van der Waals interactions between beads (mono- excellent agreement with extensive Monte Carlo simula- mers and membrane atoms) are modeled through a repul- tions using the exact interactions. sive Lennard-Jones (LJ) potential and consecutive mono- [03/11/2015 - P028] mers are subject to the Finite-Extension Nonlinear Elas- Universal behaviour for a 1+1 growth model, tic (FENE) potential. Analysing data for polymers with Waldenor R. Julvito, Washington S. Alves, different lengths, the free energy profile is noted to have ENFE - 03/11/2015 - Abstracts 39 interesting finite-size scaling properties. C. Barbosa. Pry. Rev. E 87, 032303 (2013). [3] G. Stell [03/11/2015 - P030] and P. C. Hemmer, J. Chem. Phys. 56, 4274 (1972); Non-Ergodic behaviour of a particle in long range E. A. Jagla, Phys. Rev. E 58, 1478 (1998); P. G. De- interaction with all the particles of a heat bath, benedetti, V. S. Raghavan, and S. S. Borick, J. Chem. Annibal Figueiredo, Solano Neto, Instituto de Phys. 95, 4540 (1991); W. P. Krekelberg, T. Kumar, J. F´ısica, Universidade de Brasilia In this work, we in- Mittal, J. R. Errington, and T. M. Truskett, Phys. Rev. vestigate the ergodic properties of a test particle placed E 79, 031203 (2009); J. C. P`amies, A. Cacciuto, and D. in long range interactions with all the particles of a given Frenkel, J. Chem. Phys. 131, 044514 (2009). [4] R. K. heat bath. The heat bath is constituted by N punctual Pathria, Statistical Mechanics (Pergamon Press, Oxford, Brownian particles that do not interact among themsel- 1977). ves and their trajectories may be determined by Langevin equations with gaussian random noise. The non-ergodic [03/11/2015 - P032] Solution of fractional diffusion equations with ab- behaviour and the issue about the thermalization of the sorbing boundaries, Hugo Andrade, Ernesto Ra- test particle is analysed in the framework of the Weakly poso, Laborat´orio de F´ısica Te´orica e Computacional- Non-Ergodic Statistical Physics (A. Rebenshtok& E. Bar- Departamento de F´ısica-Universidade Federal de Per- kay, J. Stat. 133, 565 (2008) Phys. DOI 10.1007/s10955- nambuco In this work we focus on the construction 008-9610-3). and solution of a fractional diffusion equation (FDE) in Many of the methods developed in this present work are one-dimensional space with absorbing boundaries. FDEs the natural development of two works: 1) Ergodicity and involve fractional derivatives in the form dα/dxα, with central-limit theorem in systems with long-range interac- α , enabling the emergence of anomalous (super- tions - EPL, 83 (2008) 30011 and 2) Truncated L’evy R diffusive)∈ behavior which cannot be taken into account flights and weak ergodicity breaking in the Hamiltonian in the conventional (Brownian) diffusion equation. The mean-field model - PHYSICAL REVIEW E 89, 022106 superdiffusive regime, in which we focus our work, arises (2014). We stress that our focus is to understand the from the solution of the FDE and also makes contact with transient regime of convergence toward a non-ergodic the distribution of the flight lengths of a L´evy flight ran- equilibrium or the sluggish convergence process toward dom walker. By solving analytically the FDE we obtain the ergodic equilibrium. the probability W (x, t) of finding the walker in a posi- Finaly we try to set up a model of CTRW (Continuous tion x at a given time t in terms of Fox H-functions. We Time Random Walk), where the ocupation time is descri- can also calculate the survival rate S(t), which measures bed by a truncated levy distribution, in order to explain the probability that the walker is still active (i.e. no- the ergodic properties associated to the test particle. nabsorbed) at a given time. We discuss the failure of the [03/11/2015 - P031] image method to solve the FDEs in a finite domain in the The Van der Waals interaction approach to the context of the violation of the Sparre-Andersen theorem. liquid-liquid phase-transition, Marcio Pazetti, We also propose an alternative approach to circumvent Universidade Federal do Vale do S˜ao Francisco (UNI- the problems related to the images technique. In parti- VASF/PE), Manuel Simoes˜ Filho, Universidade Es- cular, the long-term behavior of the survival probability tadual de Londrina (UEL/PR), Francisco Miguel da presents a time-dependence with a shift from the (Spare- Costa Junior,´ Instituto Federal do Sert˜ao Pernambu- Andersen-like) power-law to the exponential decay. Our cano (IFSPE/PE) Since the pioneering work of Stell approach is based on both analytical as well as numerical and Hemmer [1], proposing the existence of a new criti- techniques. cal point inside liquids, we have seen experiments, com- putational simulations and theory working together to [03/11/2015 - P033] understand the nature of the liquid-liquid transition [2]. Superstatistics and the quest of ensemble equi- However no definitive model of how it happens has been valence in a system with long-range interacti- yet established. Some theoretical models, mainly in one- ons, Nelson A Alves, Universidade de S˜ao Paulo, dimension, and some computational works, indicate that Rafael B Frigori, Universidade Tecnol´ogica Federal an attractive potential combined with an strongly repul- do Paran´a Superstatistics inception by Beck and sive hard core are essential ingredients for this transition Cohen was intended to provide an extension of the stan- [3]. We will present here a three-dimensional derivation dard statistical mechanics formalism into a more general of this transition. Our model is, essentially, a extension of one, focusing on describing out-of-equilibrium systems, the approach that let to the Van der Waals state equation which are most likely characterized by spatio-temporal and the gas-liquid transition. We will analytically show fluctuations of an intensive parameter. Its usual formu- that, with a small improvement, this longstanding appro- lation employs, as a working hypothesis, the argument ach also predicts the existence of a further critical point, that fluctuations evolve on a long-time scale, while the at a high pressure and a high temperature. Namely, we studied system can still be locally decomposed in many will consider the two particles Mayer cluster expansion small cells (subsystems) obeying the (equilibrium) statis- [4], and show that when we take into account not only tical mechanics characterized, for instance, by an effective the first, but also its second order terms in the inverse local (inverse) temperature β. For such systems, not only of the temperature, two critical points are obtained; the the temperature environment is considered to be a fluctu- first corresponding to the usual gas-liquid transition, and ating quantity, with probability density f (β), but also it the second corresponding to a liquid-liquid transition. [1] may carry a spatial modulation as a classical scalar field. P. C. Hemmer and G. Stell, Phys. Rev. Lett. 24, 1284 Here, the thermodynamic properties yielded by the no- (1970). [2] M. Aur´elio, A. Barbosa, E. Salcedo and M. nextensive Statistical Mechanics of Tsallis are derived, as 40 Abstracts - ENFE - 03/11/2015 a particular limit from the Superstatistics approach, for rying out a Wang-Landau sampling and performing a sta- the Blume-Capel (BC) model with infinite-range interac- tistical study of the convergence of the microcanonical tions. This model exhibits nonconcavity of the entropy as averages and of the temperature related to the peak of a function of the energy. Thus, it is well-known to pre- the specific heat. In order to use the Broad Histogram sent ensemble inequivalence, which implies on different Method, besides the computation of the usual microca- predictions for the first-order phase transition line when nonical averages of the powers of the magnetization, we taking its microcanonical or canonical description. Star- also compute, during the Wang-Landau sampling, the mi- ting from the Superstatistics approach, we numerically crocanonical averages of the number of possible changes investigate how the microcanonical limit can be recove- in the system’s state with energy E which would incre- ∆E ∆E red as a function of the nonextensive parameter q and ase (Nup (E)) and decrease (Ndn (E)) the energy by an system-size (N). Moreover, we highlight how this solu- amount ∆E. We performed simulations for several lat- tion can be compared to our previous work where BC tice sizes and from each size we took a large number of model was solved in an interpolating generalized ensem- samples to build a representative sample of the density of ble, known as Extented Gaussian Ensemble (EGE), which states and the canonical averages. We show our findings is able to continuously recover the stable microcanonical for the density of states, as well as for the finite-size sca- states as its “nonextensive” parameter γ is gradually in- ling exponents, and compare it with exact values. Our creased. In this vein, we found out that it is not necessary findings suggest that the Broad Histogram Method provi- to take the theoretically expected limit q 1 to recover des a slightly better precision on the computation of the the microcanonical states in the region between→ the ca- density of states, along with the canonical averages, than nonical and microcanonical tricritical points of the BC the one obtained within the Wang-Landau sampling. phase diagram. [03/11/2015 - P034] NON-EQUILIBRIUM Ergodic Hypothesis and the Thermalization Time for Chaotic Hamiltonian Systems with Few De- [03/11/2015 - P036] grees of Freedom, Marcio Woitek, Gastao˜ Classical limit of Jarzynski Equality, Krein, IFT-UNESP One of the fundamental assump- Josiane Oliveira Rezende de Paula, Adelcio´ tions of Classical Statistical Mechanics is the ergodic hy- Carlos de Oliveira, UFSJ - MG - Brasil The pothesis. Using this hypothesis amounts to assuming study of mesoscopic systems out of balance is actually that, in thermal equilibrium, the time average of a phase one of the most active areas of physics. Several ap- function will be equal to the corresponding microcano- proaches to the treatment of these systems have been nical average. Even though this assumption plays an developed in the last decade, highlighting the results important role in the formulation of the microcanonical of Jarzynski as well its experimental verification in ensemble, the introduction of the ergodic hypothesis was many systems. The discovery dates the nineties of always criticized. We argue that this criticism is the re- last century, where an exact relationship between non sult of an incorrect understanding about the hypothesis equilibrium work and variation of the Helmholtz free under consideration. In this article, we shall discuss some energy of the system prepared interest in two states of results that were established by means of computer simu- thermal equilibrium at temperature T. It is conjectured lations in order to provide a modern justification for using that, in the coming years, that quantum devices can the ergodic hypothesis. Moreover, we are going to explain be built using this rule, which will work in your state how the validity of this assumption can be checked for a nonequilibrium. Theoretically, it has been shown that given physical system whose numerical study can actu- quantum systems ’ratchet’ are candidates for a new ally be carried out with the aid of a computer. For such type of mesoscopic device working well in contact with a system, we shall discuss how the ergodic hypothesis al- a thermal reservoir and subjected to external driving. lows us to obtain an estimate for the time it takes to In this work, we investigated the classical and quantum reach thermal equilibrium. Our approach is based on the equilibrium relationships for the harmonic oscillator dynamical calculation of temperatures. To illustrate the and analyze the classical limit equal Jarzynski for the ideas we consider in this work, we are going to present system. The model for the study consists of a harmonic the statistical-mechanical description of two chaotic Ha- oscillator with a linear disturbance. We used Statistical miltonian systems with few degrees of freedom. These Mechanics methods based on the canonical ensemble and systems can be obtained as particular cases of certain perturbation theory to obtain the quantum analog, also classical field theories. we use quantum open system technics. We calculated the [03/11/2015 - P035] partition function, the Helmholtz free energy, stochastic Comparative study of the precision provided work and showed classical Jarzynski equality for the by the Wang-Landau Sampling and the Broad harmonic oscillator with external drive. The same Histogram Method, Paulo M.C. de Oliveira1, calculation were obtained for its quantum analogue, Alexandre Lima12, 1Instituto de F´ısica, Universidade considering the expected value of work in two areas: the Federal Fluminense; 2Centro Federal de Educa¸c˜ao Tec- work as the variation of energy and work as an operator nol´ogica Celso Suckow da Fonseca, CEFET-RJ UnED in the Heisenberg representation. The two definitions for Itagua´ı The work presented here investigates the pre- quantum work and its corresponding averages correctly cision provided by two computational techniques in the describe classical result for β 1, otherwise we are evaluation of the density of states and canonical averages in the quantum regime and Jarzynski≪ equality is not of the two-dimensional ferromagnetic Ising model. We satisfied. obtained the microcanonical and canonical averages car- ENFE - 03/11/2015 - Abstracts 41 Acknowledgments: Capes, CNPq and Fapemig. to the financial support from FAPESP. [03/11/2015 - P037] [03/11/2015 - P039] Relaxation time as a tool to characterize phase Autocorrelation Function and Dynamical transitions in dynamic processes on complex Transition on the Periodic Lorentz Gas: networks, Guilherme H. S. Costa, Silvio C. Fer- Stochastic and Deterministic Approaches, reira, Departamento de F´ısica, Universidade Federal Rafael Mateus Feliczaki, Eduardo Vicentini, de Vi¸cosa The criticality of non-equilibrium processes Pedro Pablo Gonzalez´ Borrero, Universidade in regular lattices can be investigated using the genera- Estadual do Centro-Oeste The Periodic Lorentz Gas lization of susceptibility of equilibrium systems which is a system where a point mass moves freely between a is intrinsically associated to the spatial and temporal periodical arrangement of scatterer disks, often modeled correlations. However, many complex networks are by Sinai billiards. The main interest in its study is the highly heterogeneous and requires alternative definitions diffusion coefficient, which shows the connection between of susceptibility to capture different properties of system, the billiard geometry and its statistical and dynamical generating an ambiguity in the susceptibility definition. properties. It is known that the geometric property that Moreover, spatial correlations in complex networks mostly influences the dynamics is the horizon, which becomes meaningless due to small-world property but defines whether a trajectory along corridors without temporal correlations are well defined and emerges as an collisions is possible (infinite horizon or H ) or not alternative or complementary tool to characterize phase (without horizon or H0). The dynamics is∞ hyperbolic transitions in complex networks. We analyzed the inte- and normal diffusion is observed on H0 billiards, and it is grated correlation time for two basic reaction-diffusion non-hyperbolic and anomalously superdiffusive on H . processes related to the epidemic spreading and observed The stochastic approach to diffusion in billiards has∞ that this characteristic time provides the correct critical recently gained a lot of interest. It is based on random point and exponents for the contact process (CP), a walks of particles between traps formed by adjacent model that exhibits an absorbing state phase transition, scatterers, so the diffusion coefficient is determined in on regular lattices in 1, 2 and 3 dimensions. The method function of escape time and lattice spacing between traps. was also able to identify the epidemic threshold of CP Another method to calculate the diffusion coefficient is model on synthetic scale-free networks with a power-law the integration of the velocity autocorrelation function γ degree distribution P (k) k− . Also, we applied the C(t). This technique is interesting since the C(t) decay method in a double random∼ regular network where provides information on the billiards’s dynamics as it is epidemic processes undergoes two phase transitions and known for decaying exponentially on H0 and algebrai- both were identified. Currently we are investigating cally on H billiards. Our interest is on the transition of the susceptible-infected-susceptible (SIS) model where geometries∞ between H and H0, exploring the variety of multiple transitions are also observed in finite-size configurations of a double∞ square lattice by finely tuning networks. the disks radii. In our case, we propose an escape-rate formalism, where the particles perform a continuous-time We acknowledge the financial support of FAPEMIG. step between traps but maintain correlations if they travel along corridors on H . We have introduced and [03/11/2015 - P038] ∞ Stochastic model for coexistence of ant co- demonstrated that the survival probability φ(t) provides lonies, Flavia´ Mayumi Ruziska Hirata, Taniaˆ information on the dynamics as well as the diffusion Tome,´ IFUSP We will present a stochastic model de- coefficient. By numerical simulation, φ(t), C(t) and fined on a lattice to describe the coexistence and the os- the diffusion coefficient were determined. We observed cillations of two types of ant colonies that use different similar behavior in the decay of φ(t) and C(t), which resources of the environment. This model has four states suggests that both quantities are originated from the per site, which denote occupation by elements of niche 1 same dynamics within the billiard. Nevertheless, the (state 1); occupation by individuals of colony 1 (state 2); asymptotic behavior of φ(t) shows a smooth curve which occupation by elements of niche 2 (state 3); occupation is advantageous over C(t) since the latter oscillates by individuals of colony 2 (state 4). If a site is in state strongly at long times. The divergence and convergence 1 (or in state 3) it means that it has resources for co- of the diffusion coefficient on H and H0 configurations, respectively, are also observed.∞ On H geometries with lony 1 (or colony 2). The transition probability of state ∞ 1(3) to state 2(4) is given by the probability a(c) times narrow corridors, the normal diffusion regime is still the fraction of first neighbors in states 2(4). Therefore, dominant when the phase space of the corridors are very the processes of birth of individuals of the colonies are small. However, φ(t) is sensible enough to the dynamics given by autocatalytic reactions. And colony 1(2) de- to show the algebraic tail and transition time between velops in niche 2(1) by means of a spontaneous process exponential and algebraic decay even on this limit. whose probability is b(d). From the perspective of bio- [03/11/2015 - P040] logy, this is interesting because in Amazon, it is observed A Langevin equation for a two-dimensional ro- the coexistence of several genres of ant colonies that use tating fluid, Joao˜ Paulo Galdino Pessoa, Pedro different resources, and there are studies with experimen- Hugo de Figueiredo,ˆ Luiz Carlos da Silva, DF - tal data about that. From the viewpoint of the study of UFRPE - PE - Brasil The Langevin equation essenti- stochastic processes out of equilibrium, the exploration ally describes the dynamic behavior of variables under the the model itself is interesting. We will show results ob- action of stochastic terms, due to its easy implementation tained with mean field approximation (simple and pair and phenomenological interpretation it has been applied approximations) and Monte Carlo simulations. Thanks to a wide range of problems. In this sense it occupies a 42 Abstracts - ENFE - 03/11/2015 paradigmatic position in statistical mechanics covering a [03/11/2015 - P042] wide range of applications to interdisciplinary areas such Langevin dynamics for vector variables driven as chemistry, biology, economics and quantitative linguis- by multiplicative white noise: A functional for- tics. In this communication we consider the problem of malism, Miguel Vera Moreno, Zochil Gonzalez´ floating particles on a two-dimensional fluid of viscosity Arenas, Daniel G. Barci, Universidade do Estado do α and temperature T , which rotates at a constant an- Rio de Janeiro (UERJ) We present a study on multi- gular velocity ω around a fixed axis. In addition to the dimensional stochastic processes described by a Langevin common viscous term α~v proportional to particle velo- equation with multiplicative white noise. In particular, city, the non-inertial system− introduces terms associated we address the problem of how time reversal diffusion to centrifugal and Coriolis forces. As long as the Coriolis processes are affected by the variety of conventions avai- term introduces a coupling between the Cartesian com- lable to deal with stochastic integrals. For this reason ponents the centrifugal term expelled the particles from we used a tool called formulation of functional integral, the origin. We investigates computationally and analy- where we build a functional generator of correlation func- tically the root-mean-square displacement (RMSD) ∆r tions without reference to any discretization in the Lan- behavior of particles as a function of model parameters.h i gevin equations. This type of formalism is characterized As a result of the competitive relationship between an- by a functional integration over two sets of commuting gular velocity and fluid viscosity the system exhibits th- variables, called Grassmann variables. In this sense, the ree regimes defined by different time scales. At the first stochastic process is represented in a manner similar to two regimes (t 6 2π/ω) , characterized by low angular a quantum theory of fields with contents ”bosonic”and velocities, we have a superdifusive behavior ∆r tα ”fermionic”..The usual prescriptions to define the sto- h i ∼ (α > 1/2) with a viscosity exponent dependence. On chastic integral arise in the formalism by the definitions the other hand at the third regime we get an exponential of Green functions in the sector of Grassmann variables dependence ∆r eωt. in the field theory. The stochastic calculus is codified h i∼ in our formalism in the structure of the Grassmann al- [03/11/2015 - P041] gebra. In particular we are interested in the study of Role of temperature on the global response in the systems that exhibit a noisy behavior multiplicative way, interface growth dynamics, Thiago A. de Assis, which means that the intensity of stochastic fluctuations Instituto de Fisica, Universidade Federal da Bahia - Sal- depends on the system state. We study some examples vador - BA - Brazil, Fabio´ D. A. A. Reis, Instituto such as higher order derivative Langevin equations and de F´ısica, Universidade Federal Fluminense - Niter´oi - the functional representation of the micromagnetic sto- RJ - Brazil An interesting problem in thin film sci- chastic Landau-Lifshitz-Gilbert equation. ence is a sudden change in the dynamics during the in- terface growth. For instance, this is the case of a change [03/11/2015 - P043] from sputtering to annealing in a cycle of surface clea- Critical behaviour of the monomer-monomer re- ning. Since erosion or dissolution are frequently present action model with desorption, Edio Cunha da in those processes, KPZ scaling was also observed in films Costa, Flavio´ Roberto Rusch, Universidade do Es- after high-temperature annealing, with initial deposition tado de Santa Catarina - UDESC The study of phase by sputtering. Thus, the apparently simple situation of transitions in systems far from equilibrium has aroused a sudden change in the growth dynamics may have a va- the interest of the scientific com- munity and has been riety of applications that involve KPZ scaling. growing progressively in recent years, due to its appli- The global response of the sudden changes in the inter- cation in various complex systems, including the hete- face growth dynamics is discussed using models of the rogeneous catalysis. A heterogeneous catalysis model Kardar-Parisi-Zhang (KPZ) and Villain-Lai-Das Sarma well known and used to study phase transitions is the (VLDS) classes during their growth regimes in 2 + 1 di- monomer-monomer reaction model, described by the re- mensions. We introduce scaling arguments and present action A + B AB. This catalysis reaction model dis- → simulation results to predict the relaxation of the diffe- plays a first order phase transition at the point yB =1/2, rence in the squared global roughness of the perturbed where yB represents the probability of a monomer B to and the unperturbed interfaces. Following the same li- arrive the surface. For yB > 1/2 the system evolves into nes of previous works [1-3] discussed in previous talk, we a saturated lattice by monomers of the type B, and if propose an asymptotic scaling which includes the tem- yB < 1/2 the system evolves to an A poisoned lattice. perature effects in the scaling of the correlation length. Only for yB = 1/2 the system displays an active stati- Interestingly, our results indicate a crossover from a dy- onary state in which the reaction A + B AB occurs namic where the plateau formation prevails to a dynamic indefinitely. We studied, in the present work,→ the criti- with the scaling of the correlation length of the corres- cal behaviour of this reaction model on a one-dimensional ponding VLDS model [4]. Finally, we discuss our results catalytic surface, and attach to the monomer B a desorp- making a parallel with experiments for KPZ-VLDS case tion rate α. We used the mean-field approach, at the level that may be viewed as a potential application [5]. of sites and independent pairs, as well as Monte Carlo si- [1] Y.-L. Chou, M. Pleimling, and R. K. P. Zia, Phys. mulations, and found a change in the type of transition, Rev. E 80, 061602 (2009) from a first order phase transition to a continuous phase [2] Y.-L. Chou and M. Pleimling, J. Stat. Mech. P08007 transition. This phase transition occurs between an ab- (2010) sorbing state, in which the lattice is saturated by mono- [3] T. A. de Assis and F. D. A. Aar˜ao Reis, Phys. Rev. mers of the type A, and an active steady state, in which E 89, 062405 (2014) the reaction takes place between the two monomers inde- [4] F. D. A. Aar˜ao Reis, Phys. Rev. E 81 041605 (2010) finitely. We found that the critical point (yBc ) depends ENFE - 03/11/2015 - Abstracts 43 on the value of α, and a phase diagram that separates the [1] Anteneodo & Tsallis, PRL 80, 5313 (1998); Tamarit saturated phase and the active steady state was drawn. & Anteneodo, PRL 82, 208 (2000) The static critical exponents β and ν was obtained th- [2] Moyano & Anteneodo, PRE 74, 021118 (2006) rough finite size scaling, confirming⊥ the conjecture due to Grassberger. We also obtained the dynamical critical [03/11/2015 - P046] exponents z, by introducing a suitable time variable that Solvable Small Thermal Engines, is defined as being the mean time required for the system L. A. e Defaveri, W. A. M. Morgado, PUC- to become completely poisoned, and ν , through the time Rio With the advent of modern microscopic and evolution of the order parameter (fraction|| of empty sites) nanoscopic techniques it became possible to understand at the critical point. the workings and constraints of very small systems, such as biological ones. [03/11/2015 - P044] It has become clearer in the last few years that the physics Growth exponents in a surface model with pro- of those systems is quite different from the macroscopic babilistic diffusion, Edio Cunha da Costa, Josias ones that obey the laws of thermodynamics and equili- Carvalho, Universidade do Estado de Santa Catarina brium statistical mechanics. - UDESC Surface growth models are nonequilibrium Microscopic systems are driven by fluctuations, and are systems because they present flux of particles toward the mostly in non-equilibrium states. Eventual violations of surface of some substrate. These particles are deposited the 2nd Law of Thermodynamics become possible for a and form a thin film. The mean height and the roughe- single realization of a thermodynamic process, but the ning are physical quantities of interest because they give 2nd Law is still valid for averages of many realizations. information about the growth of the film and its mild- In order to study these interesting problems, here we pro- ness. These physical quantities obeys power laws and the pose a minimal model consisting of a massive damped more interesting is the roughening power low. In the ther- Brownian particle subjected to an harmonic and quadra- modynamic limit the roughening evolves as ω tβ and, tic (k x4/4) potentials. The particle is enclosed in a box for long times, the roughening depends on the system∼ size 3 of size L(t) and in contact with a heat bath of tempera- as ω Lα. The Family - Vicsek scaling relation allows ture T (t). Having full control of the expressions for T (t) one to∼ obtain these asymptotic forms. There are different and L(t) allows us to write a wide range of cycles, from deposition models, as the ballistic deposition model, the equilibrium to non-equilibrium. Eden model and solid on solid models as well as different Our goal is to obtain the exact analytical expansions in relaxation mechanisms. In the present work, we consider orders of k for the averages of functionals such as work the random sequential adsorption and we allow the de- 3 and absorbed heat. From there we can calculate the effi- posited particle to diffuse to the nearest neighbour site ciency of our engines for different cycles. that has the lowest height. However, the diffusion occurs with some probability λ and we are interested in the ef- [03/11/2015 - P047] fect of this probability on the exponents β and α. By Absorbing phase transitions on random Voronoi employing Monte Carlo simulations and finite size sca- triangulations, Sidiney G Alves, Marcelo M de ling, we show that the exponent β depends on the values Oliveira, Silvio C Ferreira, Universidade Federal of the probability λ. de S˜ao Jo˜ao Del Rei Nonequilbrium phase transitions [03/11/2015 - P045] from an active (fluctuating) to an inactive (absorbing) Heat transport in a chain of α-XY rotators, phase in spatially extended systems is a topic of current Carlos Olivares, Celia Anteneodo, Depto. de Fi- great interest. The so-called absorbing state phase tran- sica, PUC-Rio The conduction of heat is one of the sitions (APT) arise in a wide variety of problems, for simplest but at the same time most intriguing problems example, heterogeneous catalysis, interface growth, popu- in non-equilibrium physics. Its study has put into evi- lation dynamics and epidemiology. Recent experimental dence transport anomalies for low dimensional systems. realizations in turbulent liquid crystals, driven suspensi- In other words, in the thermodynamic limit, the Fourier’s ons and superconducting vortices increased the interest law is not satisfied for low-dimensional systems. The con- in this kind of transitions. Of particular interest is how ductivity shows a dependence on the size N of the system spatially quenched disorder affects the critical behavior according to the form κ N a, where the value of a is of APT. In real systems, quenched disorder appears in dependent on the interaction∼ potential. But there are the form of impurities and defects. On a regular lattice, controversies concerning its origin. It has been argued quenched disorder can be added in the forms of random that the momentum conservation is the responsible for a deletion of sites or bonds or of random spatial variation of non-Fourier behavior, however rotator systems have dis- the control parameter. In all the cases above, one finds a played normal heat transport. On the other hand, it is change in the critical behavior of the model, with strong known that the range of the interactions brings new phe- Griffiths singularities. nomena to a system [1,2]. So, in this work, we investigate An important question is what happens when the disor- by means of molecular dynamics simulations the role that der is configurational, i.e., when the underlying graph the interaction range plays on the heat conductivity. For is not periodic, as observed in a deterministic aperiodic this purpose we consider a chain of rotators with interac- structure, or in a graph with a random connectivity such tions that depend algebraically on the distance between as the Voronoi triangulation. The Voronoi lattice repre- rotators, with a parameter that controls the range of the sents a natural way of introducing quenched coordination interactions [1]. We determine the critical range at which disorder in a lattice model, and also plays an important the systems passes from a flat temperature profile (mean role in the description of idealized statistical geometries field) to a normal profile (first neighbors). such as planar cellular structures, soap throats, etc. 44 Abstracts - ENFE - 03/11/2015 In this work, we study first-order and second-order probability is equal to any part of the area and that there absorbing-state phase transitions on the Voronoi- are no external influences, it is reasonable to say that the Delaunay lattice. Our extensive simulations confirm re- quantity of incident particles expected per area is equal cent findings of Barghatti and Vojta [1] on the effects of and corresponding. This characteristic allows these films random topological (connectivity) disorder. We observe may be applied as SSNTD detectors. It is assumed so as that such kind of disorder is irrelevant for the critical essential characteristic for SSNTD detectors that regu- behavior for models belonging to the directed percola- larity in the observed counting frequency of the incident tion and manna universality class. Using the ZGB model particles should match the expected frequency for coun- as example, we show that the coordination disorder is ting. The aim of this work is an evaluation of response not capable of changing the nature of the transition, as of count for the SSNTD detector in relation of the total occurs when uncorrelated random defects are present in count per area of incident α particles by applying the χ2 the substrate. test at a 5% level of statistical significance hoping that [1] H. Barghathi and T. Vojta, Phys. Rev. Lett. 113, the expected and observed frequencies are equivalent 120602 (2014) (null hypothesis). To demonstrate this proposition, 3 R samplesSup- of 1cm of Durolon (Bisphenol-A, used as porting Agencies: FAPEMIG and CNPq. SSNTD) packed in a dosimeter type NRPB/SSI-H were irradiated in a calibrated source PYLON RN-1023 with [03/11/2015 - P048] 3 Residual entropy and waterlike anomalies in a activity of 21kBq/m and revealed using a standard the repulsive one dimensional lattice gas, chemical attack protocol PEW-40 with subsequent Fernando Barbosa V. Silva, Marco Aurelio A. track counting using a conventional microscope with Barbosa, Fernando Albuquerque de Oliveira, magnification of 40x. In the process data acquisition it Universidade de Brasilia, Instituto Federal de Brasilia was discarded lateral area of the SSNTD and randomly Water is special fluid for its biological relevance and te- selected 10 areas (770x1028µm) along the central part chnological applications but most intriguing is that it pre- of the detector. For each region was made the total sents thermodynamic and dynamic properties with ano- count of the tracks. Based on the tracks counts, the malous (or unusual) behavior. The origin of its anoma- average and the standard deviation was determined and lous properties is actively discussed in the literature, with a relative error. Considering the average value as an 2 different thermodynamic scenarios competing to describe expected value, was applied the χ test considering the its behavior on regular and metastable regimes. Among partial counting as a observed values. The average of alternative views on water thermodynamics, it should be counts is 63 4 tracks/area, with a relative error of 7%, ± 2 relevant to mention the second critical point hypothesis the determined χ value was 2.38 and the tabulated and the singularity free scenario, which will be relevant value considering 5% of statistical significance was 3.33. 2 2 in the context of the current work. As χ9,0.05 > χcalculated, the null hypothesis is accepted. In this work, we proceed on this direction by investiga- In conclusion, the results show that the null hypothesis ting the repulsive 1D lattice gas, which is even simpler is accepted and the tracks counting in partial areas they than our previous models and presents waterlike anoma- are corresponding to a level of statistical significance lies in density, thermodynamic response functions, and of 5%. The detection response for this SSNTD can be self-diffusion constant. The model was studied through considered as valid. transfer matrix technique and Monte Carlo simulations. [03/11/2015 - P050] With the results obtained from these techniques, a con- AN APPLICATION DYNAMICS OF NON- nection between temperature of maximum density and LINEAR COMMUNITIES FOR PERFOR- GSTP was found as in a previous work with more com- MANCE EVALUATION OF VIRTUAL LE- plex models. In addition, it was also found that GSPT ARNING, Wesley Mendes Lopes da Silva, does present a residual entropy, due to phase mixing, and Francisca L´ıvia Lima Demontiezo,ˆ Francisco it is shown that this property is fundamental in determi- Felipe Moura Fontele, Danielle Luize Santos ning waterlike anomalies for the model considered here. de Oliveira, Vanessa L´ıgia Serafim, IFCE Sobral Finally, a comparison between regions with density and Permanent learning is a basic requirement for orga- diffusion anomaly indicated that this model presents so nizations to remain competitive in a market constantly called hierarchy of anomalies. changing. Along this line, companies are intensifying their action in the field of corporate education. The use OTHER TOPICS of distance education is each time bigger, providing the employees the opportunity to study in adjusted place [03/11/2015 - P049] and moment. A practice much used in distance educa- Detection Response Evaluation of a Solid tion is the asynchronous meeting, especially discussion R State Nuclear Track Detector Durolon , forums. The intention of this work was to evaluate Reginaldo Ribeiro de Aquino, Instituto de Pesqui- the effectiveness of this practice for the construction of sas Energ´eticas e Nucleares IPEN/CNEN-SP In a knowledge and the conversational abilities necessary to radioactive decay process of the 222Rn, in accordance promote the amount and the quality of the interactions with the Poisson distribution, the emitted α particle in the forums. Agreeing with some authors that question probability reaching a particular point in the active area the efficiency of the current methods of evaluation, based of the solid state nuclear track detector (SSNTD) is in the subjectivity and/or linear metrics, we present a equal to any other particle emitted reaching any point of methodology of evaluation for discussion lists, based on any area of this detector. Considering the fact that the nonlinear dynamical systems theory. The Meta Learning ENFE - 03/11/2015 - Abstracts 45 model, used in face-to-face teams, establishing the [03/11/2015 - P052] relationship between positivity and negativity with the Self-consistent statistical theory of crystal struc- performance of teams, was tested in discussion forums tures, J. N. Teixeira Rabelo, UFG - GO - Brasil of distance classes, to verify if the same parameters can In this presentation I give a short review of the state be used in the virtual environment. The Ontology of of the art in the development of the statistical theory of Language was the theoretical referential for evaluation crystal structures. It is a generalization of the unsymme- of conversational competence. The results obtained trized self-consistent field approximation proposed and showed that a positive correlation exists between po- applied earlier to crystals with Bravais lattices. This sitivity/negativity and the construction of knowledge, method is an alternative to the known self-consistent pho- as well as highlight the importance of conversational non theory of strongly anharmonic solids. It is free of any competence for the effectiveness of the forums as an perturbative schemes and can be applied with in princi- educational practice. With this research we verify that ple any type of empirical or semi-empirical interatomic the Meta Learning model can be used for evaluation of potential functions. The basic equations are derived and the performance of virtual communities of learning and solved for a few graphene-type systems. The solutions that possessing conversational competence also favors of these equations are used as a background for the in- relationships in the virtual environment. vestigation of some structural properties of these mate- rials. We calculate the equilibrium nearest neighbor dis- tances and the lattice parameters, the coefficient of ther- [03/11/2015 - P051] mal expansion, the effective amplitudes and other higher Kinetic Study of Small Particles Transport in Ra- moments of the configurational atomic phase probabi- refied Gas Media., Lucas G. L. F. Pollito, Car- lity densities. We also investigate the thermodynamics los A. B. Silva, Instituto Tecnol´ogico de Aeron´autica of these systems, and calculate the Gruneisen parameter, SP Brasil This work presents a kinetic study of small the thermal coefficient of pressure, the thermal capaci- (micrometer or nanometer scale) particles transport in ties at constant volume and pressure, the isothermal and gas media in a free molecular regime. It is based on a adiabatic compressibilities. We show here also results for Boltzmann like kinetic theory adapted to treat inelastic the energy of formation of defects like vacancies, and also collisions through the concept of scattering kernels [1]. for the surface free energy. For imperfect crystals we cal- The work focus on a generalized treatment of the drag culate the distortion of the lattice and the softening of force on a spherical particle due to its motion in a low the atomic vibrations at the vicinity of the surfaces. We density gas, with Knudsen number Kn¿¿1. The approach also give comparisions to other available theoretical, ex- Is shown to be equally applicable to particle diffusion and perimental, and simulational results. electric mobility. It is explicitly considered the influence of soft interaction potential, between the particles and the [03/11/2015 - P053] gas molecules, on the transport, compared to the trans- Anomaly in the phase diagram of the spin quan- port based on rigid sphere potential. An interaction po- tum 1/2 anisotropic Heisenberg antiferromagnet tential relevant for molecule/particle interaction, recently model with Dzyaloshinskii-Moriya interaction: A developed by Rudyak and Krasnolutski [2] is used. In- low temperature analysis, Walter E. F. Parente, teraction between gas molecules and particles is a rather J. T. M. Pacobahyba, Ijan´ılio G. Araujo,´ Uni- complex process which changes with particle size and de- versidade Federal de Roraima, Minos A. Neto, J. Ri- pends on the reflection mode on particle surface which is cardo de Sousa, Universidade Federal do Amazonas described by a reflection kernel (transition probability). In recent years, multiferroics are materials in which This requires simplified models for molecule /particle in- ferroic properties, e.g., magnetism and polar order, co- teraction. The best known is the Maxwell model which exist. Magnetic and ferroelectric ordering couple micros- introduces an accommodation parameter that measures copically or macroscopically to form the magnetic fer- the fraction of molecules diffusively reflected and consider roelectrics. These have potential applications in infor- the remaining fraction specularly scattered [3], [4]. The mation storage, actuators, sensors, and functional de- real scattering behavior is still not known and may de- vices. Perovskite BiFeO3 exhibits both “weak” ferro- pend on the particle surface roughness. In this work the magnetism and ferroelectric characteristics and has been transport is analyzed adding to Maxwell model a scatte- studied extensively in the last decade. The G-type an- ring kernel to describe the perfectly rough particle surface tiferromagnetic (AF) order of the Fe magnetic moments which will scatter the molecules into arbitrary directions exhibits a canting caused by the antisymmetric DMI un- while preserving their absolute velocity. The study made der rhombohedral R3c space group. Experimentally, the here is then compared to that made by Li and Wang[5] Dzyaloshinskii-Moriya interaction (DMI) has gained re- which used Maxwell model for the transport of almost newed interest because of the evidence to interpret an spherical silver and copper oxide nanoparticles, both, in anomalous magnetic behavior in BaCu2M2O7 (M = Si, a nitrogen gas. Ge), Yb4As3, Y V O3 SrV O3 and La2CuO4. The DMI [1] G. M. Kremer, An Introduction to the Boltzmann has gained renewed interest− because of the evidence of its Equation and Transport Processes in Gases. Springer, existence the coupling between antiferrodistortive (AFD) 2010. [2] V. Ya. Rudyak and Krasnolutski, Dokl. Phys. distortions and weak ferromagnetism where anomalies in 47, 758(2002). [3] J. C. Maxwell, Philos. Trans. R. Soc. AF vectors and band gap varying with on site Coulomb London 170, 231-256(1879). [4] Lucas G. L. F. Pollito, interaction. We will study phase diagram the quantum Disserta¸c˜ao de Mestrado, Instituto Tecnol´ogico de Ae- spin-1/2 anisotropic Heisenberg antiferromagnet model ron´autica, 2013. [5] Z. Li and H. Wang, Phys. Rev. E in the presence of a DMI (D) and a uniform longitudi- 68, 61207(2003). nal (H) magnetic field, where we have observed an ano- 46 Abstracts - ENFE - 03/11/2015 maly at low temperatures. Using the effective-field the- is then periodically exchanged with the other two modes ory with a finite cluster N = 2 spin (EFT-2) we calculate in a resonant fashion. Resonant conditions, thus a key the phase diagram in the H D plane on a simple cubic ingredient for an active interaction of the modes, are de- lattice (z = 6). We analyzed− the cases: anisotropic Hei- fined as the matching conditions for the high-frequencies senberg - case I: (∆ = 1), anisotropic Heisenberg - case II: of the slowly modulated carriers involved in the interac- (∆=0.5) and anisotropic Heisenberg - case III: (∆ = 0), tion. The decay of mode “1” into the other two (“2” and where are observed only second order phase transitions. “3”), for instance, is favored when the resonant condi- [03/11/2015 - P054] tion ω1 = ω2 + ω3 among the three high-frequencies is Quantum Random Walks in Honeycomb Lat- observed. One promptly sees that, in its canonical form, tice, Bruno Felipe Venancio, Marcos Gomes resonant conditions are heavily based on a clear separa- Eleuterio´ da Luz, UFPR - Brasil The term quan- tion of the time scales referring to the high-frequency and tum random walks (QRW) appeared in the early 1990 as the slow modulational dynamics. The present work in- the quantum analogous of classical random walks (CRW) vestigates the breakdown of the traditional modulational (Physical Review A 48, 1687, 1993). Thus, while the approximation in the three wave nonlinear interaction, CRW is defined by probability of a stochastic event oc- the wave triplet interaction. A common way to describe curs, the QRW is defined by probability amplitudes as- the interaction of three high-frequency carriers is to as- sociated with unitary transformations. One feature that sume that amplitudes and phases are slowly modulated. differs a QRW of a CRW is the mean square displace- This is the basis of the modulational approach, which ment [∆r]2. For QRW [∆r]2 t2 and to CRW [∆r]2 t, is accurate when the three wave coupling is weak. We where t is time. For an introduction∼ to QRW we sug-∼ examine the types of dynamics arising when the coupling gest the following reference (Contemporary Physics, v. rises from very small to large values. At large values we 44, n. 4, p. 307-327, 2003). The QRW can be divided detect an abrupt transition where the limited amplitude into two groups, one with an discrete time evolution, and excursions of the modulational regime reach much larger other with a continuous time evolution. However, the regions of the appropriate configuration space. Extensi- system is always implemented on discrete space (lattices ons to similar cases are also investigated. or graphs). The discrete time QRW version can be for- [03/11/2015 - P056] mulated in terms of two entirely equivalent models, the Spatial and temporal localization of light in two coin model and the scattering model, we will adopt the dimensions, C. E. Maximo´ , Ph. W. Courteille, scattering model, which we consider more physically in- R. Bachelard, Instituto de F´ısica de S˜ao Carlos, Uni- tuitive. This model consists of a particle moving through versidade de S˜ao Paulo, 13560-970 S˜ao Carlos, SP, Bra- the edges lattice and the sites act as scattering centers. zil, N. Piovella, Dipartimento di Fisica, Universit`a Thus, in a time step, the particle to focus on a site is Degli Studi di Milano, Via Celoria 16, Milano I-20133, scattering towards the edges connected to site. These Italy, R. Kaiser, Universit´ede Nice Sophia Antipolis, processes of scattering are weighted by probability am- CNRS, Institut Non-Lin´eaire de Nice, UMR 7335, F- plitudes given by scattering matrix (Physical Review A 06560 Valbonne, France Multiple scattering of waves 68, 3, 032314 (2003). Since they were proposed the QRW has been the subject of intense debates and proliferic stu- are well studied in the linear lattice. However, there are dies in the context of disorder-induced Anderson locali- few studies that dedicated to analyze them in the honey- zation [1]. However, despite several decades of research, comb lattice. Furthermore, since the QRW have been the mere existence of Anderson localization of light [2] employed in the study of electronic transport properties and its relation to another long predicted phenomenon, of some quantum systems (Physical Review Letters 94, namely Dicke super- and subradiance [3], are still not cle- 100602, 2005), we will study the in the honeycomb lat- arly understood. As most experiments are typically per- tice in order to a possible application in the theoretical formed in a three dimensional setting, models have also study of the properties electronic and the transport sys- been focused on such 3D configurations. However, both tem involving graphene and other materials that exhibit numerical and fundamental aspects of localization stron- the honeycomb pattern, for example carbon nanotubes gly depend on the dimension of the explored system. For and fullerenes. In this work we present a formulation for this reason, we have focused our efforts on a 2D system. the QRW in honeycomb lattice, compare the classical and Two-dimensional set-up can be obtained, e.g., with a di- quantum random walks and found the expected behavior sordered arrangement of scatterers in microwave cavities, for mean square displacement in those two systems. in photonic crystals, near surface plasmons or with laser- [03/11/2015 - P055] cooled atoms located in an off-resonance optical cavity. Beyond the modulational approximation in The main advantage of that the reduced dimensionality the wave triplet interaction, Paulo Iorra, also allows for a direct comparison between two regimes Samuel Marini, Eduardo Alcides Peter, Renato of scattering, one corresponding to a scalar model of light, Pakter, Felipe Barbedo Rizzato, Universidade Fe- the other one corresponding to a vectorial model of light, deral do Rio Grande do Sul One of the most well ac- where the polarization of the wave needs to be taken into cepted and well established models for nonlinear wave in- account. Then we are able to switch between the scalar teraction is based on the wave triplet concept . The wave or vectorial regime, between the presence or the absence triplet arises as an entity of physical significance, as one of polarization degrees of freedom, and the presence or selects the three most prominent modes of an oscillatory the absence of near field terms, making it an ideal tool system and investigates the coupled dynamics of these to investigate the role of polarization in localization and selected modes as an isolated subsystem. In general, one subradiance. Performing scaling analysis we observe in mode starts off with a sizeable energetic content, which both cases long lived atomic modes of the scattering, yet ENFE - 03/11/2015 - Abstracts 47 only the scalar case exhibits Anderson localized modes. Oral sessions (11:00-12:30) Investigating the reasons for the absence of localization in cold atoms ensambles, it appears that both the coupling of polarization and the presence of near field terms are able to prevent long lifetimes and Anderson localization. LONG RANGE INTERACTIONS We finally show that, albeit extremely long mode lifeti- mes are present only in localization regime, this lifetimes [03/11/2015 - 11:00 - Room Vit´oria] and their localization length are uncorrelated [4]. Statistical Mechanics of Systems with Long- Range Interactions, Y. Levin, R. Pakter, F. Rizzato, T. N. Teles, F. P. C. Benetti, A. C. Ribeiro-Teixeira, Instituto de F´ısica, UFRGS Systems with long-range forces behave very diffe- rently from those in which particles interact through short-range potentials. For systems with short-range [1] P. W. Anderson, Physical Review. 109, 1492 (1958). interactions, for arbitrary initial conditions, the final [2] S. E. Skipetrov, I. M. Sokolov, Physical Review Letters stationary state corresponds to the thermodynamic 112, 023905 (2014). equilibrium and can be described equivalently by either [3] R. H. Dicke, Physical Review. 93, 99 (1954). a microcanonical, canonical, or a grand-canonical en- [4] C. E. M´aximo, N. Piovella, Ph. W. Courteille, R. semble. On the other hand, for systems with unscreened Kaiser, R. Bachelard. To be submitted. long-range forces, equivalence between ensembles breaks down. Isolated long-range interacting systems — in [03/11/2015 - P057] thermodynamic limit — do not evolve to the usual Stall in a numerical wind tunnel, Maxwell-Boltzmann equilibrium, but become trapped in Paulo Victor Santos Souza, Instituto Federal a non-ergodic stationary state which explicitly depends do Rio de Janeiro - RJ - Brasil, P M C de Oliveira, on the initial particle distribution. In this talk, a Universidade Federal da Integra¸c˜ao Latino-Americana theoretical framework will be presented which allows In this work, we introduce a new method for determi- us to predict the final stationary state to which a ning the behavior of the drag force. We have used this long-range interactioning system will evolve. The theory method in order to compare the drag and lift coefficients is able to quantitatively account for both density and for a simple model of wing within numerical wind velocity distributions in the stationary state, without tunnels. The inspiration comes from an experimental any adjustable parameters [1,2,3]. result: a small, light ball falls on air; its speed increases, reaches a maximum, decreases and finally stabilizes. [1] Y. Levin, R. Pakter and T. N. Telles, Phys. Rev. Lett. This surprising behavior is due to the gradual formation 100, 040604 (2008). of the so- called von K´arm´an street of vortices: while [3] R. Pakter, and Y. Levin, Phys. Rev. Lett. 106, it is not completely formed, the transient drag force 200603 (2011); F. P. da C. Benetti, T. N. Teles, R. Pak- is smaller than the known steady state value and ter, and Y. Levin, Phys. Rev. Lett. 108, 140601 (2012); the ball can reach speeds higher than its final value. T. N. Teles, F. P. da C. Benetti, R. Pakter, and Y. Le- In building the numerical wind tunnel we solved the vin, Phys.Rev. Lett. 109, 230601 (2012); R. Pakter, B. Navier-Stokes equation by the finite difference method Marcos, and Y. Levin, Phys. Rev. Lett. 111, 230603 and successive relaxations. The initial condition is the (2013).F. P. C. Benetti, A. C. Ribeiro-Teixeira, R. Pak- flow around the obstacle immersed in an incompressible ter, and Y. Levin, Phys. Rev. Lett. 113, 100602 (2014). fluid with vanishing velocity (obeying the same equation [3] Y. Levin et al., Phys. Rep. 535, 1 (2014). for vanishing Reynolds number). At this moment, the wind tunnel is turned on with a constant, finite free [03/11/2015 - 11:20 - Room Vit´oria] stream speed (corresponding to a Reynolds number of Ergodic properties of systems with the order of 1,000). After a transient time, we observe long-range interactions., C´ınthia He- the formation of a street of vortices in the fluid portion lena Silvestre, IF/Universidade de Bras´ılia, behind the wing, the so-called von K´arm´an street. In Tarc´ısio Marciano da Rocha Filho, cifmc- particular, we investigated the relationship between the IF/Universidade de Bras´ılia We study the ergodic behavior of the coefficients and the attack angle. Our properties of a two-dimensional self-gravitating system results suggest the manifestation in the wind tunnel of a using molecular dynamics simulations by applying three well-known phenomenon in aviation, the stall crisis. different tests for ergodicity: a direct method comparing the time average of a particle momentum to ensemble averages, sojourn times statistics for cells in momentum space and the dynamical functional method. These methods are also applied to a short-range interacting system (a hard-sphers gas in two dimensions), and the Hamiltonian mean-field model, for comparison purposes. Our results show that a two-dimensional self-gravitating system takes a very long time to establish ergodicity. This time is independent of particle number, at variance with what is observed in the Hamiltonian mean-field model. 48 Abstracts - ENFE - 03/11/2015 [03/11/2015 - 11:35 - Room Vit´oria] with the system size N, diverging when N goes to infi- Dynamical threshold in the relaxation of long- nity. By contrast, in long-range systems, the interplay range systems, Romain Bachelard, IFSC-USP, between wave-particle interaction and spatial inhomoge- Brazil, Michael Kastner, NITheP, Stellenbosch, neity drives the system to nonequilibrium stationary sta- South Adrica The dynamics of systems with mean- tes that generically exhibit temperature inversion. We field interaction, when all the particles interact with equal demonstrate this mechanism in a simple mean-field mo- strength, is characterized by very long equilibration ti- del and in a two-dimensional self-gravitating system. Our mes: Indeed, the system gets trapped in quasi-stationary work underlines the crucial role the range of interparti- states, where macroscopic quantities (temperature, mag- cle interaction plays in determining the nature of steady netization, etc) evolve very slowly toward their equili- states out of thermal equilibrium. We have shown that brium value. The lifetime of these states generally in- nonequilibrium stationary states with temperature inver- creases with the system size and, as a consequence, the sions are the typical outcome of a perturbation acting for time for the system to reach equilibrium diverges in the a short time on a clustered equilibrium state of a long- thermodynamic limit. range interacting system. This rather surprising result We here investigate the equilibration of lattice systems can be explained in terms of Landau damping and ve- with long-range pair interactions, decaying like 1/rα with locity filtration, suggesting that temperature inversions the distance r. The long-range regime corresponds to may occur whenever the dynamics is collisionless up to α < d, with d the dimension of the system. We cha- the relevant timescales. This mechanism may be actually racterize the relaxation times and show that long-range relevant to understand temperature inversions observed lattice systems also exhibit quasi-stationarity, as well as in nature. This work was partially supported by CNPq relaxation times that diverge with the size of the system. and published in its complete version at Physical Review However, upon varying the interaction range α, we find E (Rapid Communications) 92, 020101(R) (2015). evidence for the existence of a threshold at α = d/2, at which the relaxation behaviour changes qualitatively and [03/11/2015 - 12:05 - Room Vit´oria] Zeno dynamics and Cooperative Shielding from the corresponding scaling exponents switch to a different long range interaction, Giuseppe Luca Celardo, regime. Since our observation is based on the behavi- Universita’ Cattolica del Sacro Cuore We analyze both our of both a quantum and a classical system, investi- single particle transport models with long range hop- gated analytically and numerically, for ferro- and anti- ping and many-body systems with long range interaction. ferromagnetic interactions, we conjecture this threshold First we discuss a paradigmatic one dimensional disorde- and some of its characteristic properties to be universal. red model with both nearest-neighbor and 1/rα hopping [03/11/2015 - 11:50 - Room Vit´oria] amplitudes. Such a model is relevant for different phy- Temperature inversion in long-range interacting sical systems and it can be directly implemented in ion systems, Tarcisio N. Teles, Instituto de Fisica, Uni- traps, where α can be tuned from zero to a value larger versidade Federal do Rio Grande do Sul. than one. In case of long range hopping, in the large Departamento de Ciˆencias Exatas e Sociais Aplicadas, system size limit, we show the existence of a subspace Universidade Federal de Ciˆencias da Sa´ude de Porto where the dynamics occurs as if long range hopping was Alegre., Shamik Gupta, Pierfrancesco Di Cintio, absent or reduced to short range. We named such effect Lapo Casetti, Dipartimento di Fisica e Astronomia Cooperative Shielding. Cooperative shielding strongly af- and CSDC, Universit`adi Firenze, and INFN, sezione fects transport properties: while long range hopping is di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, usually thought to destroy localization, strong signatu- Italy Temperature inversions occur in nature, e.g., in res of localization can be found in the shielded subspace. the solar corona and in interstellar molecular clouds: So- Next, many-body quantum spin-1/2 systems with long- mewhat counterintuitively, denser parts of the system are range interaction, are discussed. Contrary to the common colder than dilute ones. We propose a simple and appe- expectation that long-range interaction should always in- aling way to spontaneously generate temperature inver- duce an instantaneous spread of information in the ther- sions in systems with long-range interactions, by prepa- modynamic limit, the shielding effect may lead to a finite ring them in inhomogeneous thermal equilibrium states velocity of the propagation of information or even the and then applying an impulsive perturbation. This work entire freezing of the dynamics, even in absence of disor- is motivated by an attempt how such a counterintuitive der. This shielding phenomenon can be related to the effect may spontaneously arise in nonequilibrium states, quantum Zeno effect, which refers to the freezing of the unveiling its minimal ingredients and the underlying phy- dynamics into invariant subspaces in a system under con- sical mechanism. We start with asking a simple yet phy- tinuous measurement. Thus long-range interaction plays sically relevant question: What happens if an isolated a role similar to a measuring apparatus. macroscopic system in thermal equilibrium is momenta- rily disturbed, e.g., by an impulsive force or a “kick”? If QUANTUM SYSTEMS & CONDENSED the interactions among the system constituents are short- MATTER ranged, collisions redistribute the kick-injected energy among the particles, yielding a fast relaxation to a new [03/11/2015 - 11:00 - Room Tubar˜ao] equilibrium, with a Maxwellian velocity distribution and Dual landscapes in Anderson localization on dis- a uniform temperature across the system. Is the scena- crete lattices, M. L. Lyra, Universidade Federal de rio the same if instead the interactions are long-ranged? Alagoas - Brazil, S. Mayboroda, University of Minne- For long-range systems, collisional effects act over a cha- sota - USA, M. Filoche, Ecole Polytechnique, France racteristic time that, unlike short-range systems, scales In Anderson localization, electronic states are expo- ENFE - 03/11/2015 - Abstracts 49 nentially localized despite the absence of classical con- timating the γC using the elementary SCP (a common finement, this localization being explained as originating practice for experimentalists) may be relevant. from the destructive interference of waves reflected in the [1] R. G. Forbes, J. H. B. Deane, Proc. R. Soc. Lond. A, random atomic potential. Despite numerous theoretical 463 2907 (2007). advances, such as the prediction by the scaling theory of [2] R. G. Forbes, Proc. R. Soc. A 469, 20130271 (2013). the lower critical dimension of the Anderson transition, [3] T. A. de Assis, Sci. Rep. 5, 10175 (2015). there was until recently no general formalism capable to [4] T. A. de Assis, J. Vac. Sci. Tech. B 33, 052201 accurately pinpoint the spatial location of these localized (2015). modes for any given potential, nor to predict the exact [5] M. T. Cole et al., Sci. Rep., 4 4840 (2014). energy at which delocalized modes would begin to form. Recently, a new theory has been proposed, unveiling in [03/11/2015 - 11:35 - Room Tubar˜ao] continuous media a direct relationship between any speci- Hydrodynamic Decay of Decorated Quantum fic realization of the random potential and the correspon- Vortex Rings, L. Moriconi, Instituto de F´ısica - Uni- ding location of localized states. It has been demonstra- versidade Federal do Rio de Janeiro The decay of quan- ted that the boundaries of the localization regions, which tum vortex rings in HeII, visualized with the help of solid cannot be deduced by directly looking at the bare ran- hydrogen particles trapped in their cores (which are re- dom potential, can be accurately retrieved as the valleys gions of the flow with local pressure drop) [1,2], has been lines of a “hidden landscape”u(x) which is the solution of a problematic issue within the standard approach based a Dirichlet problem with uniform right-hand side for the on the two-fluid model of superfluidity [3]: the large drag same Hamiltonian. exerted on the vortex rings by the flow of normal fluid In this talk, we show that not only the exact same theory past the hydrogen particles would ultimately lead to de- can be extended to the case of a tight-binding Hamilto- cay times that mismatch the ones measured in the labora- nian defined on a discrete lattice, but also that, contrary tory, besides non-observed dynamical phenomena (as vor- to the continuous case, two different types of localization tex ring rotation and contour deformation). Taking into occur here. First, localization of low energy states can be account the so-called “triple structure”of quantum vor- predicted using a discrete analog of the landscape u(x) tex rings, as predicted by Kivotides et al. [4], we discuss defined in the continuous situation. Secondly, the dis- a phenomenological solution of vortex ring decay puzzle, creteness of the system also triggers a strong localization which is based on the fact that the vortex ring energy of states of typical wavelength of the order of the lattice loss is accounted for not only by mutual friction, but also spacing (corresponding to the top of the band for a perio- by the viscous dissipation and sweeping of the flow struc- dic potential). We show that this localization can also be tures produced from the vortex ring backreaction on the studied in the framework of the landscape theory, with normal component of the surrounding superfluid. a different operator than the original Hamiltonian and, References respectively, a different landscape. [1] G.P. Bewley, D.P. Lathrop, and K.R. Sreenivasan, Na- [03/11/2015 - 11:20 - Room Tubar˜ao] ture 441, 588 (2006). Improving the extraction of characteristic [2] G.P. Bewley and K.R. Sreenivasan, J. Low Temp. field enhancement factors from non-linear Fowler- Phys. 156, 84 (2009). Nordheim plots: role of the irregular morpho- [3] K.W. Schwarz, Phys. Rev. B 31, 5782 (1985). logy of large area conducting field emitters, [4] D. Kivotides, C.F. Barenghi, and D.C. Samuels, Sci- Thiago A. de Assis, Instituto de F´ısica - Universidade ence 290, 777 (2000). Federal da Bahia - Salvador - Ba - Brazil We show that the dependence between the effective emission area [03/11/2015 - 11:50 - Room Tubar˜ao] and the macroscopic electric field, FM , allow for the in- Electron-soliton dynamics in chains with cu- troduction of a new correction, ω, in the elementary slope bic nonlinearity, Messias Oliveira Sales, characterization parameter (SCP) for extracting the cha- Francisco Anacleto Barros Fidelis de Moura, racteristic field enhancement factor, γC , from (precise) Instituto de F´ısica - UFAL The lattice vibrations orthodox cold-field electron emission measurements [1,2]. and its coupling with the electronic dynamics (the First, we discuss the effects of the Hurst exponent (H) on electron-phonon interaction) plays relevant roles on the the local electric field distribution and the slope of the effective electronic transport. In our work, we consider Fowler-Nordheim (FN) plot when considering the cold fi- the problem of electron transport mediated by the eld electron emission properties of rough Large-Area Con- coupling with a solitonic wave. Our model consists of ducting Field Emitter Surfaces (LACFESs) [3]. We dis- a one-electron moving in an unharmonic lattice and we cuss also the case where the local macroscopic enhance- will focus on the existence of an electro-soliton pair. In ment factors, γ, are Gaussian-distributed [4], as has been our model, we will consider a one-dimensional unhar- experimentally determined for the potential candidates of monic lattice with a cubic interaction between nearest cold-field electron emission applications [5]. In this case, neighboring sites. The electron-lattice interaction was using the recent developments in cold-field electron emis- introduced by considering the energy hopping following sion theory, we found that for the typical experimental the (SSH) approximation, i.e. a linear function of the range of 1 V/µm FM 10 V/µm, the nonlinearities distance between neighboring atoms. We will solve that are often observed≤ in≤ cold-field electron emission ex- numerically the dynamics equations for the electron periments may appear in JM -FM -type Fowler-Nordheim and lattice and compute the dynamics of an initially (FN) plots. Finally, our results show that depending on localized electronic wave-packet. Our results suggest the distribution of γ over the LACFES, the error in es- that the solitonic waves that exist within this nonlinear 50 Abstracts - ENFE - 03/11/2015 lattice can control the electron dynamics along the Oral sessions (14:30-16:05) entire lattice. We will study in details the formation of a electron-soliton state that can move along the chain. This mobile electron-soliton pair can be a key ingredient CRITICAL PHENOMENA to the charge transport in a nonlinear chain. Moreover, we will investigate in details which intensity of the [03/11/2015 - 14:30 - Room Tubar˜ao] Nematic phase in the J1-J2 square lattice Ising electron-lattice interaction necessary to promote the model in an external field, Alejandra Guerrero, appearance of this electron-soliton pair. Our calculations Daniel Stariolo, Departamento de F´ısica, Universi- suggest that, even for strong electron-lattice coupling, dade Federal do Rio Grande do Sul, Noe´ G. Almarza, we can find an electronic dynamics non mediated by Instituto de Qu´ımica F´ısica Rocasolano, CSIC, Madrid, solitonic waves. Spain The J1-J2 Ising model in the square lattice is [03/11/2015 - 12:05 - Room Tubar˜ao] a minimal model with competing nearest-neighbor and Thermodynamics of a Relativistic Generalization next-nearest-neighbor interactions. Its phase diagram in of Ginzburg-Landau Theory, Carlos Bonin, Fe- the temperature versus κ = J2/ J1 plane has three pha- deral University of Technology - Paran´a(UTFPR-PG) ses: ferromagnetic and a striped| phase| at low T and a Superconductivity is a key milestone for technology ad- disordered phase at high T. The nature of this phase di- vance. Superconduting magnets are used in Magnetic agram has been debated in the last 20 years. Instead, Resonance Imaging Machines and for steering of the be- the effects of an external field on the phase diagram have ams in particle accelerators such as the Large Hadron been much less studied. We have studied it by two appro- Collider. Although there is no unified description for aches: the Cluster Variation Method (CVM) and Monte “high-temperature supercondutors, low-temperature su- Carlo simulations. The use of the CVM in the square perconductors are reasonably well-understood. The un- approximation leads to the presence of a new equilibrium derstanding of low-temperature superconductors started phase, not previously reported for this model: an Ising- with phenomenological theories, such as those of the Lon- nematic phase, which shows orientational order but not don brothers and the famous Ginzburg-Landau theory. positional order, between the known stripes and disorde- Finally, a deeper understanding of the underlying me- red phases. Monte Carlo simulations are in qualitative chanism for superconductivity was achieved in the cele- agreement with the CVM results, giving support to the brated Bardeen, Cooper and Schrieffer Theory of Super- presence of the new Ising-nematic phase. Phase diagrams conductivity (BCS Theory). Later on, using techniques in the temperature-external field plane are obtained for of Statistical Mechanics, Gor’kov was able to recover the selected values of the parameter κ which measures the re- Ginzburg-Landau action (or Free Energy) starting from lative strength of the competing interactions. From the BCS Theory. In this talk we follow a similar path. We CVM in the square approximation we obtain a line of start from a relativistic generalization of BCS Theory second order transitions between the disordered and ne- proposed by Bertrand and, through Gor’kov’s and Ber- matic phases, while the nematic-stripes phase transitions trand’s statistical approach, we review as a Relativistic are found to be of first order. The Monte Carlo results Generalization of Ginzburg-Landau Theory can be achie- suggest a line of second order nematic-disordered phase ved. Then, from the effective action of the relativistic the- transitions in agreement with the CVM results. Regar- ory, we use methods of Finite Temperature Field Theory ding the stripes-nematic transitions, the present Monte (also known as Statistical Quantum Fields) to compute, Carlo results are not precise enough to reach definite con- to some degree of approximation, relevant thermodyna- clusions about the nature of the transitions. mic quantities, such as the partition function and the free [03/11/2015 - 14:50 - Room Tubar˜ao] energy density. Furthermore, quantum statistical effects, Annealed Ising model with site dilution on such as the dependence of the “vaccum”polarization and self similar structures, Vanessa S. T. Silva, self-energy with the temperature, may be presented. Roberto F. S. Andrade, Instituto de F´ısica, Univer- sidade Federal da Bahia, Silvio R. Salinas, Instituto de F´ısica, Universidade de S˜ao Paulo We consider an Ising model on the triangular Apollonian network (AN), with a thermalized distribution of vacant sites. The sta- tistical problem is formulated in a grand canonical en- semble, in terms of the temperature T and a chemical potential µ associated with the concentration of active magnetic sites. We also investigate the analogous mo- del on the diamond hierarchical lattice (DHL). We use a well-known transfer matrix method, with a number of adaptations, to derive a set of (non linear, discrete) maps for the free energy and other auxiliary variables along successive generations of the hierarchical structure. The major changes as compared to the quenched or ordered situations amounts to formulating the statistical problem in terms of an effective Hamiltonian in a grand-canonical ensemble, depending on temperature T and a chemical potential µ, which is associated with the concentration of occupied sites. This is justified by the fact that, in a ENFE - 03/11/2015 - Abstracts 51 thermalized system, the orientational variables are trea- sed. First, it will be shown that the glass of hard spheres ted on the same basis as the positional disorder degrees of can be mapped in a network of points connected with freedom. From the numerical iteration of the recursion nonlinear springs [1]. Using this idea, it is shown that relations, we obtain various thermodynamic quantities. to understand quantitatively stability of a glass at a mi- In the µ limit, we reproduce the results for the croscopic level, the presence of weakly interacting pairs uniform models:→ ∞ in the AN, the system is magnetically of particles must be included. This approach allows us to ordered at all temperatures, while in the DHL there is predict various non-trivial scaling behaviour of the elas- a ferromagnetic-paramagnetic transition at a finite value ticity and vibrational properties of glasses. Some of these of T . Magnetic ordering, however, is shown to disappear exponents are tested numerically and experimentally in for sufficiently large negative values of the chemical po- colloidal glasses. It also gives a spatial interpretation to tential. recent calculations in high-dimensions [2]. [03/11/2015 - 15:05 - Room Tubar˜ao] [1] C. Brito and M. Wyart, J. Chem. Phys. 131, 024504 Information entropy of classical versus explosive (2009) percolation, Tiago M. Vieira, Gandhi M. Viswa- [2] E. DeGiuli, E. Lerner, C. Brito, M. Wyart , Proc. nathan, Luciano R. da Silva, UFRN - RN - Brasil Natl. Acad. Sci. USA, 111, 17054 (2014) Percolation is used to model diverse phenomena, ran- [03/11/2015 - 15:35 - Room Tubar˜ao] ging from porous media to social interactions. There is a Short-time Monte Carlo simulation of a well-known phase transition associated with percolation, frustrated Ising model in two dimensions, characterized by the emergence of a giant cluster at the Adauto Jose´ Ferreira de Souza, Universidade critical point, comparable in size to the entire network. Federal Rural de Pernambuco The frustrated Ising Besides the classical percolation, in which the giant clus- antiferromagnet with first- and second-nearest-neighbor ter emerges from a completely random process of adding interactions is studied within the framework of short- edges to a network, in recent years a novel type of per- time non-equilibrium behavior on square lattices. The colation, called explosive, has been studied. In explosive Hamiltonian reads percolation, the addition of edges includes a choice pro- cess aimed to retard the emergence of the giant cluster. = J s s J s s , (1) H − 1 i j − 2 i k Looking for a method of studying phase transitions of i,j i,k percolating systems without the explicit use of order pa- hXi hXi rameter (relative size of the network’s largest cluster), we where si = 1, J1 < 0, J2 < 0, and the first summation is analyze the Shannon entropy associated with the cluster carried out± only over nearest-neighbor pairs of spins whe- size probability distribution. It’s known that at the criti- reas the second one is over next-nearest-neighbor pairs of cal point the cluster size distribution is a power-law, i.e. spins. Notice that the Hamiltonian given by Eq. (1) is there are clusters of all sizes, so one expects the infor- frustrated on square lattices. mation entropy to attain a maximum. As expected, our Recently, the phase diagram of this model system was ob- results show that the entropy attains a maximum at this tained through an effective-field theory with correlations point for classical percolation. Surprisingly, for explosive [Phys. Rev. E 91, 032145 (2015)] and approximations percolation the maximum entropy does not match the based on different cluster sizes in the R = J1/ J2 versus critical point. Moreover, we show that it is possible de- temperature plane. It was found that the phase| | tran- termine the critical point without using the conventional sitions between the antiferromagnetic and paramagnetic order parameter, just analysing the entropy’s derivatives. phases (R> 0.5) close to R = 0.5 are of first order and turn into second− order for R >− R , with (T , R ) [03/11/2015 - 15:20 - Room Tubar˜ao] tcp tcp tcp Marginal stability, heterogeneous force distribu- the coordinates of the tricritical point. Obviously, the tion and vibrational properties in hard sphere effective-field theory does not give any information on glasses, Carolina Brito, Universidade Federal do the true critical exponents. Rio Grande do Sul (UFRGS), Eric de Giugli, Univer- In this work, the critical properties of the frustrated Ising sity of New York (NYU), Edan Lerner, University of antiferromagnet, Eq. (1), is investigated through short- Amsterdam, Mattieu Wyart, University of New York time Monte Carlo relaxation on square lattices. The main goal is to locate the line separating the paramagnetic (NYU) When the temperature of a liquid is decreased phase from the antiferromagnetic phase ( 0.5 R 0) in such a way that crystallization is avoided, the resul- − ≤ ≤ ting material is a glass or an amorphous solid. There are and obtain estimates to the critical exponents along this two sets of open questions concerning this subject. The line. The values of the critical exponents to R in the range [ 0.4, 0] are compatible with the Ising universality class first is a central problem in soft and condensed matter − physics that aims understanding how a liquid becomes in two dimensions. Therefore, no signal of a tricritical rigid at the glass transition. Although there are many point was found in the range of R investigated. scenarios to describe this transition, even in the simplest [03/11/2015 - 15:50 - Room Tubar˜ao] glasses - hard spheres -, what confers mechanical stability Discontinuous absorbing phase transitions: Mi- at large density is a matter of debate. The second set of nimal mechanisms and generic finite size scaling, questions is related to the properties of the amorphous Carlos E. Fiore, Marcelo M. de Oliveira, M. G. material which is generated in this transition: when in E. da Luz, IFUSP Motivated by recent findings, we the glass phase the material present different properties first discuss the existence of a direct and robust me- in respect to its crystal phase, as for example transport chanism providing discontinuous absorbing transitions in and vibrational properties. short range systems with single species, with no extra In this work these two set of questions will be addres- symmetries or conservation laws. We consider variants 52 Abstracts - ENFE - 03/11/2015 of the contact process, in which at least two adjacent at the other side of the barrier after many generations. particles (instead of one, as commonly assumed) are re- Finally I will discuss coevolution in a spatially distribu- quired to create a new species. Many interaction rules are ted population of predators and prey that engage into an analyzed, including distinct cluster annihilations, parti- arms race. In all cases the results of simulations will be cle diffusion, and a modified version of the original pair compared with empirical data. contact process (PCP). Through detailed time dependent numerical simulations we find that for our modified mo- [03/11/2015 - 14:50 - Room Vit´oria] dels, the phase transitions are of first-order, hence con- Metapopulation dynamics in a complex habitat: trasting with their corresponding usual formulations in the role of resource aggregation and dispersal the literature, which are of second-order. By calculating strategy, Eduardo H. Colombo, Celia Antene- the order-parameter distributions, the obtained bimodal odo, PUC-Rio Habitat heterogeneity exists due to the shapes as well as the finite scale analysis reinforce coe- spatial distribution of resources, water, shelter, etc. This xisting phases, so a discontinuous transition. These fin- variability fragments the habitat in regions, known as dings strongly suggest that above particle creation requi- patches, which are favorable or not for population growth. rements constitute a minimum and fundamental mecha- This leads to the emergence of a metapopulation struc- nism determining the phase coexistence in short-range ture made of sub-populations that remain connected due contact processes. Also, a phenomenological but gene- to individuals’ movements [1]. We present a general mo- ral finite size scaling theory is proposed for discontinuous del [2] to study the role of habitat spatial structure and nonequilibrium phase transitions into absorbing states. dispersal strategy in metapopulation dynamics. The lo- Analogously to the equilibrium case, we show that quan- cal dynamics is driven by fundamental mechanisms, con- tities such as, response functions, cummulants, and equal sisting of a logistic expression plus multiplicative noises area probability distributions, all scale with the volume, that take into account demographic and environmental thus allowing proper estimates for the thermodynamic li- fluctuations [3]. Nonlocality is introduced in a general mit. To illustrate these results, distinct lattice models way, considering that individuals dispersal can be diffu- displaying nonequilibrium transitions – including above sive (random) or selective (habitat dependent). Further- examples– are investigated. Our findings (allied to previ- more, the ecological landscape of favorable patches is ge- ous numerical studies in the literature) strongly point to nerated like a L´evy dust, which allows to build a range an unifying discontinuous phase transition scaling beha- of patterns, from dispersed to clustered ones. As regards vior for equilibrium and this important class of nonequi- the habitat spatial structure, the results show a critical librium systems. degree of clusterization to preserve the population. The [1] Carlos E. Fiore Phys. Rev. E 89, 022104 (2014); generalization of animal dispersal enables us to show the S. Pianegonda and C. E. Fiore, J. Stat. Mech. 2014, importance of a mixed strategy, i.e. the combination of P05008 (2014); M. M. de Oliveira, M. G. E. da Luz and random movement and direct routes between favorable C. E. Fiore, (submitted). regions. In a general way, our results highlight the inter- play between noise and spatial coupling schemes in the asymptotic behavior of the total population size. POPULATION DYNAMIC [1] Hanski I., and Ovaskainen O., Nature 404:755–758 (2000) [03/11/2015 - 14:30 - Room Vit´oria] [2] Colombo E.H., Anteneodo C., ArXiv-1503.08168 Integrating genetics and geography in population (2015) dynamics, Marcus Aloizio Martinez de Aguiar, [3] Ovaskainen O., Meerson B., Trends in Ecology & Evo- Ayana de Brito Martinas, UNICAMP - Instituto de lution , 25(11):643-652 (2010) F´ısica Gleb Wataghin, Yaneer Bar-Yam, New England Complex Systems Institute, Cambridge, MA, USA, Mi- [03/11/2015 - 15:05 - Room Vit´oria] cael Nagai, UNICAMP - Instituto de Biologia The A non-phenomenological model of competition evolution of a population depends on the way its individu- and cooperation to explain population growth als interact with one another and with the environment. behaviors, Fabiano L. Ribeiro, UFLA This work In spatially distributed populations interactions are local proposes a non-phenomenological model of population and specific features of the geography can affect its gene- growth that is based on the interactions among the in- tic evolution. In this talk I will first discuss an individual dividuals of a population. When there is competition based model of speciation that is driven by local mating between the individuals, the model proposed reaches the and does not require the existence of geographic barriers Malthus, Verhulst, Gompertz, Richards, Bertalanffy and separating the population in isolated groups. Each indi- power-law growth models. And when there is coopera- vidual will be characterized by its position in space and tion, the model reaches the von Foerster growth model by a genome composed of several biallelic genes. In the and also presents a regime of divergence of the population model mating is possible only if the individuals are suf- at a finite time. This approach explains the Allee effect as ficiently close to each other in space (local mating) and an emergent behavior of the cooperative and competitive also similar genetically (assortative mating). Depending interactions among the individuals. The Allee effect is the on the parameters of the model the population can evolve characteristic of some populations of increasing the popu- into separate species even in the absence of natural selec- lation growth rate in a small-sized population. Whereas tion. Using the same theoretical framework I will show the models presented in the literature explain the Allee simulations for ring species, where an initially localized effect with phenomenological ideas, the model presented population expands in two directions around a physical here explains this effect by the interactions between the barrier in such a way that the two expanding fronts meet individuals. The model is tested with empirical data to ENFE - 03/11/2015 - Abstracts 53 justify its formulation. Another interesting macroscopic del. For this, we associate the age of a tree with its ro- emergent behavior from the model proposed is the ob- bustness and hence to its degree of flammability, so that servation of a regime of population divergence at a finite much younger or older trees, shall be more susceptible to time. It is interesting that this characteristic is observed burning than those at the ripe age. Particularly, we in- in humanity’s global population growth. vestigate the effects of wildfires in the most simplest case The presentation is based on two recent published papers: of single-species forests focusing on the dynamic regime 1. RIBEIRO, F. L. ; RIBEIRO, K. N. . A one dimen- where the probability of interaction between fires is null. sional model of population growth. Physica. A (Print), In such scenario, the density of trees can evolves in large v. 434, p. 201-210, 2015. 2. RIBEIRO, F. L. . A Non- time scales to one of two possibles steady state attrac- phenomenological Model of Competition and Coopera- tors, dense forest or savana forest, regardless of the initial tion to Explain Population Growth Behaviors. Bulletin configuration of trees. The time dependent profile of the of Mathematical Biology (Print), v. 77, p. 409-433, 2015. density of trees and its steady-state age-frequency histo- I would like to acknowledge the financial support from grams and fire-size distributions were estimated through FAPEMIG. various simulations and the records analyzed according [03/11/2015 - 15:20 - Room Vit´oria] to the model parameters. Evolving cellular automata for diversity genera- The dense forest state is characterized by a high den- tion and pattern recognition: deterministic versus sity of trees with an uniform age histogram for almost all random strategy, Marcio Argollo de Menezes, classes, except for the one of the very young trees and UFF - Niteroi - Brazil, Edgardo Brigatti, UFRJ - those of the senescence period, the later exhibiting an RJ - Brazil, Veit Schwaemmle, University of Southern exponential decay. Moreover a typical exponential decay Denmark - Odense - Denmark Microbiological systems for the fire-size distribution function appears indicating evolve to fulfil their tasks with maximal efficiency. Mo- that the presence of a massive number of mature trees delling efforts depend crucially on this assumption and prevents the spread of large fires. On the other hand, the adaptation is the key element for evolution to take place. savana forest state is characterized by a low density of The immune repertoire is a remarkable example of an very young trees exhibiting an power-law like behavior for adaptable, evolving system whose main role is the de- the fire-size distribution function. In short, the inclusion fense of living organisms against pathogens (antigens), of correlation between the age of trees and its flamma- where the distinction between self and non-self is made bility even in a mono-species forest environment, leads by means of molecular interactions between proteins and to a possible dynamic phase transition between dense fo- antigens, triggering affinity-dependent systemic actions. rest to a savanna forest state. An outline of the phase Specificity of this binding and the infinitude of potential diagram according the model parameters is discussed. antigenic patterns call for novel mechanisms to generate [03/11/2015 - 15:50 - Room Vit´oria] antibody diversity. Inspired by this problem, we deve- Percolation and cooperation with mobile lop a genetic algorithm where agents with antibody in- agents: Geometric and strategy clusters, formation encoded as bit strings evolve their repertoire Mendeli H. Vainstein, Carolina Brito, Je- in the presence of random antigens (encoded as random ferson J. Arenzon, UFRGS - RS - Brasil We study strings) and reproduce with affinity-dependent rates. We the conditions for persistent cooperation in an off-lattice develop a population dynamics with stationary popula- model of mobile agents playing the Prisoner’s Dilemma tions constrained by size-dependent, Verhulst-like death (PD) game with pure, unconditional strategies (C: rates. We ask what is the best strategy to generate di- cooperate, D: defect)[1]. Each agent has an exclusion versity if agents can rearrange their strings a finite num- radius rP that accounts for the population viscosity, and ber of times. We find that endowing each agent with an an interaction radius rint that defines the instantaneous inheritable cellular automaton rule for performing rear- contact network for the game dynamics. The agents rangements makes the system more efficient in pattern- undergo random diffusion and the strategy evolution matching than if transformations are totally random. In follows the finite-population analog of the replicator the former implementation, the population evolves to a dynamics. We show that, differently from the rP = 0 stationary state where agents with different automata ru- case (pointlike agents), the model with finite sized agents les coexist. presents a coexistence phase with both cooperators and [03/11/2015 - 15:35 - Room Vit´oria] defectors. Moreover, there are also two absorbing phases Interplay between wildfires and forest age struc- in which either cooperators or defectors dominate. We ture in steady state., Rebeca Cabral de Novaes, provide, in addition, a geometric interpretation of the Gustavo Camelo Neto, Sergio´ Coutinho, Univer- transitions between phases and present a phase diagram sidade Federal de Pernambuco Stationary forests can of the PD dynamics as a function of both parameters, be characterized by a spatiotemporal distribution of spe- rP and rint. To determine the phases, we performed cies of trees in respect of its location and age. Several a finite-size analysis and studied the probability of external factors like wildfires, recurrent plagues and fo- percolation of D clusters as a function of time. In rest managements for harvesting of timber, should per- analogy with lattice models, the geometric percolation turb the dynamics of the evolution of the populations of of the contact network (i.e., irrespective of the strategy) tree species, superimposed to the inherent topographical enhances cooperation. More importantly, we show that and hydrological factors as well as the climate seasonal the percolation of defectors is an essential condition variations. We investigate the interplay between the dis- for their survival. Differently from compact clusters of tribution of long-term and large-scale forest fires and the cooperators, isolated groups of defectors will eventually forest tree age distribution, using a cellular automata mo- become extinct if not percolating, independently of their 54 Abstracts - ENFE - 03/11/2015 size. Our results are robust for a great range of mobilities Oral sessions (17:05-18:15) and of the temptation parameter in the PD game. [1] M. H. Vainstein, C. Brito and J. J. Arenzon, Phys. Rev. E., 90, 022132 (2014). BRAINS AND NEURONS [03/11/2015 - 17:05 - Room Vit´oria] If the brain is critical, what is the phase tran- sition?, Mauro Copelli, UFPE - PE - Brazil Neuronal avalanches were experimentally observed in vitro a decade ago, lending support to a long-held con- jecture that the brain as a dynamical system might be operating near a second-order phase transition. Nontri- vial statistics, such as power law distributions and other scale-invariant properties, have been the essential con- nection between the theory of critical phenomena and neurophysiological data. Many models which have been used to simulate neuronal collective behavior share com- mon features, displaying a phase transition from an ab- sorbing (quiescent) to an active (but otherwise unstruc- tured) phase. Most of these belong to the directed perco- lation universality class, which has served as a theoretical workhorse in the field. I will discuss the strength and limitations of this theoreti- cal framework in light of experimental results, which have since been extended to in vivo experimental setups, in- cluding both anesthetized and non-anesthetized animals. More generally, I will highlight the need of theoretical de- velopments in Neuroscience, which offers theoretical phy- sicists a fertile ground for interdisciplinary research. For instance, how can we model the long-range time correlati- ons and universal scaling functions observed in the brain activity of freely-behaving animals? Or, given that cur- rent recording techniques severely undersample neuronal activity, is it possible to come up with a model that yields scale-invariant statistics even under similar sampling con- ditions? Can we reconcile these ideas with the plethora of oscillatory activity which is observed in the brain? [03/11/2015 - 17:25 - Room Vit´oria] Resilience and Synchronization of Brain Networks, Mauro Copelli, UFPE - PE - Bra- zil [03/11/2015 - 17:45 - Room Vit´oria] Thermo-Comparative Analysis of Texts: Translations and Target Readerships, Henioˆ Henrique Aragao˜ Regoˆ , Departamento de F´ısica/Instituto Federal de Educa¸c˜ao, Ciˆencia e Tecnologia do Maranh˜ao - IFMA, S˜ao Lu´ıs/MA/Brazil, Lidia A. Braunstein, Departamento de F´ısica, Fa- cultad de Ciencias Exactas y Naturales, Instituto de Investigaciones F´ısicas de Mar del Plata (IFIMAR), Universidad Nacional de Mar del Plata-CONICET, Mar del Pla, H. Eugene Stanley, Center for Polymer Studies/Boston University/Boston/MA/USA, Sasuke Miyazima, Department of Natural Sciences/Chubu University/Kasugai/Aichi/Japan Scaling laws have been an important topic in the physics community across a wide range of Fields. The dynamics of several complex systems in biology, economics, and natural phenomena, have been described with relative success using scaling laws. Scaling phenomena also emerge in the analysis of data associated with human behavior, especially those containing a statistically distributed component, such as the number of links in the World Wide Web or the size of ENFE - 03/11/2015 - Abstracts 55 cities. In current research, the analysis of scaling in data Paulo, Caixa Postal 369, 13560-970, S˜ao Carlos, SP, continues to produce new and interesting Findings in a Brazil Associated to the equilibrium Gibbs state of a variety of scientific fields. In another multidisciplinary given critical classical system in d dimensions we can asso- approach, the usual concept of energy can be related to ciate a special quantum mechanical eigenfunction defined the frequency of word occurrence in a text, therefore, in a Hilbert space with the dimension given by the num- its probability distribution can also be related with ber of configurations of the classical system and compo- the temperature concept. We propose a comparative nents given by the Boltzmann weights of the equilibrium ¨thermo-analysis¨technique that allow us to determine probabilities of the critical system. This class of eigen- the academic level of a text and its corresponding functions are generalizations of the Rokhsar-Kivelson wa- target readership in any given language. We apply this vefunctions, initially proposed for the dimer problem in technique to a large number of books by several authors 2 dimensions. In particular in two dimensions, where and examine how the vocabulary of a text changes when most of the critical systems are also conformal invariant, it is translated from one language to another. Unlike the such functions exhibit quite interesting universal featu- uniform results produced using the Zipf law, using our res. The entanglement entropy of a line of contiguous ¨word energydistribution¨ technique we find variations in variables (classical spins), is given by the classical mu- the power-law behavior. We also examine some common tual information of d = 1 quantum chains, and the en- features that span across languages and identify some tanglement spectrum of the two dimensional system are intriguing questions concerning how to determine when given by the amplitudes of the ground-state eigenfunction a text is suitable for its intended readership. of the quantum chain. We present a conjecture showing [03/11/2015 - 18:00 - Room Vit´oria] that the mutual information of the quantum chains in Properties of semantic networks derived some appropriate basis (we called conformal basis) show from automatic generated word embeddings, a universal behavior with the size of the line of the en- Marco Idiart, Instituto de F´ısica, UFRGS, Aline tangled spins (subsystem size). This dependence allow us Villavicencio, Rodrigo Wilkens, Instituto de to identify the conformal charge of the associated clas- sical critical system (used to define the d = 2 quan- Inform´atica, UFRGS Recently Mikolov et al.[1] proposed a very successful neural network algorithm tum eigenfunction) or the quantum critical chain. We to automatically extract a vector representation of the will also make a connection with a possible classifica- words of a language (word embeddings) from a training tion of the 2d Rokhsar-Kivelson wavefunctions following set composed of large collections of representative texts. the Renormalization-Group ideas of scaling invariant sys- From the word embeddings with simple vector algebra tems. it is possible to derive a series of language properties [03/11/2015 - 17:25 - Room Tubar˜ao] such as word similarity, plural and gender operations, Temperature and entropy oscillations of a gas compositionality of multiword expressions, etc. For in circular geodesic motion in the Schwarzschild instance, the similarity of two words in the schema is field, Gilberto M. Kremer, Winfried Zimdahl, simply the cosine between their vector representations. Universidade Federal do Paran´a, Universidade Federal do Therefore the similarity matrix of the whole lexicon Esp´ırito Santo The present work is devoted to a global can be viewed as a semantic network, where words equilibrium configuration on the background of the static correspond to nodes and the distances between them Schwarzschild metric. We consider a Boltzmann gas with are the weighted edges. In this work we characterized its center of mass moving on a circular geodesic of this statistically the semantic network derived from Mikolov’s metric, and we study the equilibrium thermodynamics of vector embeddings for different spatial dimensions and this system as seen by a comoving observer on the geo- compare it with studies performed in semantic networks desic. The lowest-order gravitational effects that a freely from manually constructed thesaurus. In addition we falling observer can detect locally are conveniently des- show that the eigenvalues distribution of the word cribed with the help of Fermi normal coordinates. These embeddings covariance matrix follows a power law. This coordinates are Minkowskian on the geodesic, while gra- indicates that the dimension of the word embeddings vitation at lowest order manifests itself in quadratic cor- space cannot be well defined via representation reduction rections in the space-like geodesic distance, orthogonal methods such as principal component analysis. We to the observers time-like trajectory. We apply a descrip- examine separately the networks of nouns and verbs, tion of this type to the gas motion, admitting additio- given their different characteristics, and to what extent nally a pure spatial rotation. This corresponds to using these are reflected in the resulting network properties. a “proper reference”frame up to second order. Fixing [1] Tomas Mikolov, Kai Chen, Greg Corrado, and Jef- this frame determines, via Tolmans law, the temperature frey Dean. Efficient Estimation of Word Representations profile of the gas as measured by a central, geodesic ob- in Vector Space. In Proceedings of Workshop at ICLR, server. It turns out that the comoving observer measures 2013. oscillations of the temperature and other thermodynamic quantities, like entropy, with frequencies that are double the frequencies known from test-particle motion in the FUNDAMENTAL ASPECTS Schwarzschild field. We apply this scheme to the gas dy- namics in the gravitational fields of the planets of the [03/11/2015 - 17:05 - Room Tubar˜ao] Universal behavior of Shannon and R´enyi mu- Solar System as well as to strong-field configurations of tual information of 1d system and some special 2d neutron stars and black holes. quantum eigenfunctions., Francisco C. Alcaraz, Instituto de F´ısica de S˜ao Carlos, Universidade de S˜ao 56 Abstracts - ENFE - 04/11/2015 [03/11/2015 - 17:40 - Room Tubar˜ao] Landau theory for uniaxial nematic, biaxial ne- matic, uniaxial smectic-A, and biaxial smectic-A phases, Dora Izzo, Mario´ Jose´ de Oliveira, Insti- tuto de F´ısica da UFRJ, Instituto de F´ısica da USP We consider a lyotropic liquid crystal and search for a model able to predict smectic, nematic and isotropic phases: an extension of the model proposed by de Gennes and Prost (1), where no smectic phases are found. In that order, we use a Ginzburg Landau mean field approach to obtain these phases. This method also takes into account opti- cal anisotropy for it predicts the existence of uniaxial and biaxial domains that have been observed experimentally (2), (3). Solutions of the mean field equations rely on analytical and numerical calculations. We choose a par- ticular set of parameters of the free energy and obtain a sequence of two-dimensional phase diagrams, which show the appearence of the different domains. The transition between the biaxial nematic and biaxial smectic is conti- nuous as well as the transition between the nematic pha- ses and the transition between the smectic phases. The transition from uniaxial nematic and uniaxial smectic is continuous with a tricritical point. The tricritical point may be absent and the entire transition becomes con- tinuous. The four phases meet at a tetracritical point. Although, the Landau free energy was set up to describe the smectic-A phase, it can also be applied to the lamel- lar phase due to the correspondence concerning symmetry between lamellar and smectic phases. (1) de Gennes,P. G., Prost, J., The Physics of Liquid Crystals (Clarendon Press, Oxford), 1974. (2) Boden,N. and Holmes, M.C. ,Chem.Phys.Lett 109,76 (1984). (3) Oliveira,E.A., Li´ebert,L and Figueiredo Neto, A.M. ,Liq.Crys.5,1669 (1989). ENFE - 04/11/2015 - Abstracts 57 Plenary talks (8:30 - 10:00) nition of the independent (density) variables in the micro- canonical ensemble. We illustrate this point by revisiting the paradigmatic examples given by Ruffo, Mukamel, and PLENARY SESSION coworkers: (i) A fully-connected spin-1 Blume-Capel mo- del, which is known to display a phase diagram with a [04/11/2015 - 08:30 - Room Vit´oria] tricritical point; (ii) An Ising chain with competing short Active matter: An introduction and some recent and long-range interactions, which displays second and advances, Hugues Chate´, CEA - Saclay, France,& first-order phase transitions for suitable choices of para- Beijing Computational Science Research Center, China meters (see A. Campa, T. Dauxois, and S. Ruffo, Phys. In this talk, I will introduce the new, fast-growing, in- Repts. 480, 57-159, 2009). Although long-range interac- terdisciplinary field of active matter and present some tions pose notoriously difficult problems, we show that recent important advances. in these elegant and paradigmatic cases there is no di- Active matter is the term now used by physicists to sagreement between calculations in the usual canonical designate out-of-equilibrium systems in which energy is and microcanonical ensembles. The crucial point is the spent in the bulk, locally, to produce persistent mo- recognition that the microcanonical ensemble describes tion/displacement. Examples abound, not just within an isolated system, in terms of suitable thermodynamic living systems (bird flocks, fish schools, collective motion density variables, while the usual canonical ensemble is of cells, etc.) but also, increasingly, in man-made, well- characterized by the thermodynamically conjugate field controlled, non-living systems such as micro- and nano- variables. Details of our arguments are described in V. B. swimmers, active colloids, in vitro mixtures of biofila- Henriques and S. R. Salinas, Recovering the equivalence ments and motor proteins, etc. of ensembles, arxiv: 1501.04029v1 (and in part II, to be I will show some striking experimental/observational posted soon). examples and then proceed to give an account of our cur- rent understanding of some of the simplest active matter models, which consist of self-propelled particles locally aligning their velocities. In this context, the fluid in which the particles move is neglected, and one speaks of ”dry ctive matter”. I will argue that these models do have experimental relevance, in addition to being important per se, much as the Ising model is important in statisti- cal mechanics. I will show that a wealth of new physics arises, which calls for further theoretical studies. [04/11/2015 - 09:00 - Room Vit´oria] Complex human contact networks: Em- pirical data, modeling and dynamics, Romualdo Pastor-Satorras, Universitat Poli- tecnica de Catalunya In recent years, the possibility to access large digital databases, as well as the development and deployment of large scale monitoring frameworks, has allowed to peer for the first time into the statistical properties of human behavior. Surprisingly, the patterns of human activity have been shown to be extremely bursty, characterized by long tailed distributions, in opposition to the Poissonian behavior expected from traditional mathematical approaches. Apart from the insights that these discoveries have in the description and hypothetical predictability of human behavior, they are most relevant due to the direct connection between the patterns of human activity and the topological description of the representative social networks. Here we will discuss recent modeling efforts designed to un- derstand and reproduce the empirical properties of social networks, as well as their effects on simple dynamical processes. [04/11/2015 - 09:30 - Room Vit´oria] Recovering the equivalence of statistical ensem- bles, Vera B. Henriques, Silvio Salinas, Instituto de F´ısica, Universidade de S˜ao Paulo The equivalence of thermodynamic results in the canonical and the mi- crocanonical ensembles has been questioned in a number of calculations for lattice spin models with equivalent- neighbor (mean-field) interactions. We show that these claims of inequivalence are related to an inadequate defi- 58 Abstracts - ENFE - 04/11/2015 Posters (10:00-11:00 / 16:05-17:05) bottow-up model , the possible mechanisms that take place in these time events. For that we make use of a conductance-based integrate-and-fire model with a spike- BIOLOGICAL PHYSICS timing-dependent-plasticity (STDP) rule. We train the network with a special-temporal pattern, similar to pre- [04/11/2015 - P001] vious experimental works, and search for the network to- Effects of habitat fragmentation on biodiver- pology and plasticity effects. We use networks with three sity patterns, Jose´ Alvino de Lima Filho, different topological connections: random, regular square Viviane Moraes de Oliveira, Universidade Federal lattices and small world, with different connectivity and Rural de Pernambuco, Fernando Fagundes Fer- connection probabilities, and change gradually the para- reira, Universidade de S˜ao Paulo The understanding meters of the STDP model in order to control the plasti- of how species diversity is related to habitat conditions is city action. a major issue in ecology. In this sense, spatial heteroge- We have verified that the minimum frequencies neity can have great influence on the number of species. that allow a self-sustained activity is closely dependent The diversity of species in natural communities is also of network size. Namely small networks demand higher related to the rate at which energy flows through the frequencies than bigger ones, and usually asynchronous ecosystem. There is an increasing interest in understan- irregular (AI) states are only found in large networks. ding the effects of habitat fragmentation on biodiversity Assuming that this kind of state is important for mo- patterns. In this work we investigate the effects of habi- deling, since it is observed in an awake cortex, we also tat destruction on species diversity patterns by using a added poissonian processes in a fraction of neurons ran- spatial computer simulation model in which species com- domly chosen, mimicking a network of bigger size. This pete for limiting resources on habitats with spatial he- produced the expected AI behavior and turned possible terogeneity. In our model each site of the lattice holds the use of realistic synaptic weights and the acquisition n resources and the amount of each available resource of firing rates of 10 Hz. This work is still in progress, ∼ is obtained from a uniform distribution. Each species k and the step we are implementing now is the fine tuning is characterized by a set of n half-saturation constants of the stimulus-response system. This will allow us to Kkj , where j denotes the resource label. The efficien- evaluate the time scales for which the network is able to cies of each species in the management of resources are respond to the stimulus. taken into account by using the fitness function of spe- [04/11/2015 - P003] cies k on site i, which is given by fki = min(Ri1/(Kk1 + How to perform Monte Carlo simulations for pro- Ri1), Ri2/(Kk2 + Ri2),...,Rin/(Kkn + Rin)). In order tein chains far from equilibrium concerning to the to study the effects of habitat fragmentation on biodiver- solvent, Joao˜ Paulo Dal Molin, Antonio Caliri, sity patterns we assume that a proportion p of the sites DFQ - FCFRP - USP When we perform Monte Carlo can not be colonized. The distribution of unsuitable si- (MC) simulations in order to emulate the protein folding tes is controlled by a fractional Brownian motion, which process we handle with a chain-solvent system. The first produces spatially correlated landscapes. We investigate component is a finite (nanometric) sub-system, while the the behavior of the species-area relationship and the dis- second one, the solvent (the thermal reservoir), is a large tribution of species abundance for some values of p and and homogeneous system well characterized by the ther- also by varying the degree of spatial autocorrelation of modynamic equilibrium. However, at nanoscale domain, the landscape. Our results indicate that both the level of thermal fluctuations emerge as a fundamental feature, be- spatial correlation and the degree of fragmentation have cause thermal noise plays an important role over chain’ a strong influence on the shape of the species-area relati- configurations. In order to incorporate this aspect in our onship and also on the distribution of species abundance. MC sampling we adopt the Tsallis weight instead of the [04/11/2015 - P002] usual Boltzmann factor [1]. Once we choose the Tsallis’ Temporal Correlation Between Stimulus weight, the entropic index q is regarded as a dynamical And Response In Spiking Neural Networks, variable; q values are associated with instantaneous de- Eduarda Demori Susin, Beatriz Eymi Pimentel grees of freedom n of an evolving chain. As the chain pac- Mizusaki, Rubem Erichsen Junior,´ Leonardo king goes on, the number of inter-residue contacts chan- Gregory Brunnet, UFRGS It is well known that ges, so n becomes a function of the globule surface, which temporal processing on time scales of tens and hundreds is roughly estimated by the square of the gyration radius of milliseconds plays an important role in simple and RG. In our point of view, q reflects the effect of local complex sensory problems in the brain, such as, motion thermal fluctuations on the chain, which are more criti- discrimination, and speech recognition. Recent studies cal over compact configurations (q>1) than over those showed that cultured cortical networks can be shaped extended ones (q 1). The effect of q>1 on the transi- by the history of an external stimulus by reflecting tion probability, faced→ to the standard Boltzmann factor, the temporal patterns of these stimuli in the network is quite equivalent to the conventional exponential factor dynamics, suggesting that cortical networks are capable in which its argument has been effectively decreased (in- of learning the stimulus time scales. Although one might creased temperature of the thermal reservoir). Therefore, know that synaptic plasticity may be a key process in for more compact configurations, larger q values are ne- this phenomenon, the detailed process underlying it still eded. Which is equivalent to the situation in which the demands for an explanation. chain is submitted to a little higher temperature than the In this work we are concerned in exploring, pre-established thermal reservoir temperature [1]. The mathematically and computationally, by means of a net effect on the chain evolution is that wrongly com- ENFE - 04/11/2015 - Abstracts 59 pacted configurations can escape more easily from ener- les in the solution, which has the result of increasing their getic/steric traps. In order to stress our point of view effective concentrations. In particular, the importance of we will show an extended set of MC simulations for the crowding in protein folding is of great interest in biophy- folding process performed with both statistical weights. sics, once the crowding effect can accelerate the folding [1] Dal Molin JP, da Silva MAA, Caliri A, Effect of local process, given that a compact folded protein will occupy thermal fluctuations on folding kinetics: A study from the less volume than an unfolded protein chain. However, perspective of nonextensive statistical mechanics, Phys. crowding can reduce the yield of correctly folded protein Rev. E 2011,84:041903. by increasing protein aggregation. [04/11/2015 - P004] Then, we try to answer the question above by showing Convergence of the transfer-integral technique that all those aforementioned complex interactions can in the framework of Peyrard-Bishop model, be well-described by a straightforward generalization of Mateus Rodrigues Leal, Gerald Weber, Departa- a simple Ising-like model, previously proposed by Bakk mento de F´ısica, UFMG The Peyrard-Bishop model is and Høye to account for protein folding under the in- a simplified physical statistics method proposed in 1989 fluence of a polar solvent. There proteins are described for calculating key properties of DNA and RNA molecu- in a close analogy with a one-dimensional homopolymer, les. Currently, it is widely used with several theoretical where relevant degrees of freedom are ascribed by contact techniques such as molecular dynamics and path inte- maps built from protein residues. Thus, closed contacts grals, but its main application still lies with its original are assigned a binding energy while open contacts pre- method the transfer-integral technique. It also used to sent several configurations of equal (zero) energy. Addi- predict hydrogen bonds and stacking interaction in oligo- tionally, we have introduced a new long-range coopera- nucleotides from melting temperature experiments, com- tive/competitive interaction term that properly models plementing experimental techniques such as NRM and inter-protein interactions (crowding). As an outcome the X-ray diffraction. In 1997 Zhang et al [Phys. Rev. E 56, model exhibits both cold and warm unfolding, which are 7100] showed that due to the form of the DNA stacking properly affected by the crowded environment as alre- interaction potential the integral equation, which is cen- ady verified experimentally for several small globular pro- tral to the method, suffers from a numerical convergence teins. problem which leads to a divergence in the partition func- [04/11/2015 - P006] tion. The workaround to this divergence problem is either Stability of neural network activity regi- to add a fixed upper limit to the integral equation or to mes achieved by the balance between ex- add specific terms to the model Hamiltonian. These ad- citatory and inhibitory synaptic scaling, ditional terms could be an angle dependence or a stress Beatriz Eymi Pimentel Mizusaki, Eduarda term as suggested by some authors. These workarounds Demori Susin, Rubem Erichsen Jr., Leonardo have allowed the development of the Peyrard-Bishop mo- Gregory Brunnet, UFRGS Neural circuits, such del into a highly successful method, still a clean solution as the cerebral cortex, display a resting basal activity to the divergence problem would be highly desirable. Re- that never ceases. In order to better understand the cently Estrada et al [J. Comp. Appl. Math. 236, 3561, functioning of these systems, and how they may process 2012] developed an analytical technique where the 1D information, it takes to understand what is needed for Hamiltonian is mapped into 3D which they claim would the maintenance of an uncorrelated basal activity. This be able to resolve the divergence problem. But a numeri- is the so-called background state, in which an input cal implementation of this technique was not attempted representation may be embedded while avoiding patholo- and it is still unclear if the problem has really been sol- gical regimes such as network-wide synchronization. One ved. Here we analyse in detail the influence of the various of the processes that is considered to be critical for this approaches to the divergence problem on the eigenvalue is the experimentally observed plasticity mechanism of spectrum. We implement a numerical algorithm for the homeostatic synaptic scaling. This phenomenon consists method proposed by Estrada et al and compare them on the reaction by the network upon a sudden activity with the proposed workarounds to evaluate the effects on disturbance, in which its synaptic weights are adjusted the eigenvalue spectrum. so that a set spiking frequency can be regained. In Funding: CPNq, Capes and Fapemig neurons of the visual cortex, it is seen that the ampli- [04/11/2015 - P005] tude of excitatory signals is enhanced if the activity is How can macromolecular crowding affect protein damped, and decreased if the activity is augmented. The stability ?, Rafael B Frigori, Universidade Tec- inhibitory connections follow the opposite direction of nol´ogica Federal do Paran´a The interior of cells is a change. While the effects of the plasticity on excitatory crowded environment, this can make molecules in cells connections have been recently studied, the concurrent behave in radically different ways than in test-tube as- inhibitory plasticity and their results over the network says. Therefore, the study of biochemical processes under balance, as well as the following interferences with other realistically crowded conditions is very important, since long-term plasticity mechanisms, are not clear. Our these conditions are a ubiquitous property of all cells and work is based on the analysis of a mean-field model crowding may be essential for the efficient operation of adapted to account for the synaptic scaling and the metabolism. Notably, the size of such effect is non-linear, comparison of its results with those of detailed numerical so macromolecules are much more strongly affected than simulations of integrate-and-fire neural networks to are small molecules as amino acids. Most likely, it is due assert the stability of the basal activity state. We find to the fact that high concentrations of macromolecules necessary relationships between macroscopic parameters, reduce the volume of solvent available for other molecu- such as the ratio between the recurrent and feedforward 60 Abstracts - ENFE - 04/11/2015 connections according to the frequency to which the rent classifications repeat protein family. Repeat proteins network is expected to converge in order to keep the have the advantage of the folding pathways that are li- activity from diverging. kely to be schematized. In this article were selected in [04/11/2015 - P007] 1213 proteins deposited in the Brookhaven Protein Data GU mismatch stability investigation by a me- Bank suggested by Andrade and collaborators [3], divi- soscopic model, Tauanne D. Amarante, Gerald ded into six tandem repeat class with different lengths Weber, Departamento de F´ısica, Universidade Fede- from 20 to 50 residues, wherein we investigate characte- ral de Minas Gerais, Belo Horizonte-MG- Brazil The ristics of fractal geometry. Using the Mean Field Theory guanine-uracil (GU) mismatch, as well as being the most of Flory, the mass-size scale exponent analysis shows that common base pair after the canonical base pairs CG and the exponent is δ = 2.15. The average packing density 3 AU, plays an important role in RNA by acting as a re- tends to ρ = 0.86a.u./A with q-Gaussian distribution cognition site for biomolecules. According to Crick, a to the masses of proteins with entropic index q = 1.90. GU mismatch would be formed by two hydrogen bonds. The findings indicate self-organized criticality as to the However, later experimental measurements showed that explanation protein folding and no hydrophobicity scale the stability of this base pair depends on its sequence con- can be relevant to these proteins. Therefore, the fractal text. For instance, NMR data indicates that the number geometry behaves between a two-dimensional wire crum- of hydrogen bonds varies depending on the GU mismatch pled and packed spheres randomly in the percolation th- flanking base pairs, and when arranged in tandem with reshold. another GU also exhibits a dependence on the strand [1] E. M. Marcotte, M. Pellegrini, T. O. Yeats and D. direction. The mesoscopic model proposed by Peyrard Eisenberg, J. Mol. Biol. 293 (1999) 151-160. and Bishop [1] seems ideal to investigate the stability of [2] P. Enkhbayar and R. H. Kretsinger. J. Proteomics GU mismatch due to its ability to distinguish the contri- Bioinform. 7 (2014) 139-150. bution of stacking interaction and hydrogen bonds. We [3] M. A. Andrade, C. Perez-Iratxeta and C. P. Ponting, adapted this model to deal with context-dependent hy- J. Struct. Biol. 134 (2001) 117-131. drogen bonds of GU mismatches by allowing the para- meters to take into account the dependence on the neigh- [04/11/2015 - P009] Integration properties of the Burak & Fi- bours pairs and strand direction. The optimization of ete continuous attractor network model, the model parameters was obtained through a set of ex- Samoel Renan Mello da Silva, Roger P. M. perimental melting temperatures data [2] by using the da Silva, Marco Aurelio Pires Idiart, Instituto technique developed by our group [3,4]. As expected, in de F´ısica, Universidade Federal do Rio Grande do Sul most contexts the Morse potential obtained for GU mis- Observed in 2005 by Hafting et al, grid cells are matches indicate hydrogen bond strengths comparable to neurons in the medial entorhinal cortex of rats that AU base pairs. While, in particular, our prediction of a have the property of firing when the animal is at specific single hydrogen bond for GUpUG tandem configurations periodic positions in a 2D space such that the map of agrees with NMR measurements. Our results also suggest their activity forms a hexagonal grid pattern. In one that the stability of GU terminal pairs could be attribu- of the classes of models that are used to theoretically ted to hydrogen bonds as we found that Morse potentials describe this observation, called continuous attractor were generally larger than for AU base pairs. networks, a hexagonal pattern present in a neural [1] M. Peyrard and A. R. Bishop; (1989) Phys. Rev. Lett. network is moved accordingly in response to the animal 62 2755-2757; displacement. One of this models, proposed by Burak [2] J. L. Chen, A. L. Dishler, S. D. Kennedy, I. Yildirim,, & Fiete (2009), uses neurons sensitive to the animal B. Liu, D. H. Turner and M. J Serra; (2012) Biochemistry, velocity and direction to move this pattern. The network 51(16), 3508-3522; proposed, however, is very well structured in the sense [3] G. Weber, N. Haslam, N. Whiteford, A. Pr¨ugel- that only four angles (north, south, west and east) are Bennett, J. W. Essex and C. Neylon; (2006) Nature Phy- present and that their locations in the network are very sics 2 55-59; specific. In the present study, we compare the model [4] G. Weber, J. W. Essex and C. Neylon; (2009) Nature performance when this preferred directions are located at Physics 5 769-773; not so organized positions and also when their preferred Funding: CPNq, Capes and Fapemig angle are subjected to noise. Moreover, we also analyze [04/11/2015 - P008] the hexagonal pattern against defective and single bump Fractal analisys of tandem repeats protein, patterns aiming to show that the first one is less suitable Fernando S. Silva, Marcelo A. Moret, Marcelo to integrate space displacement in the presence of noise. C. Santana, Universidade Estadual do Sudoeste da The hexagonal pattern is the one that maximizes activity Bahia UESB - Brasil; Programa de Modelagem Compu- in the network and can therefore be more robust to local tacional, SENAI Cimatec Salvador -Brasil; Universidade perturbations. Salvador, UNIFACS Salvador - Brasil Proteins are bi- opolymers essential to life, constituted by a long amino [04/11/2015 - P010] acid sequence. They may be formed from up to 20 diffe- Boundary effects in the Burak & Fi- rent kinds of amino acids. A significant portion of these ete continuous attractor network model, proteins, about 14% et all [1,2], they have repeated seg- Roger Prochnow Moreira da Silva, Samoel ments of amino acids. These repetitions occur when in Renan Mello da Silva, Marco Aurelio´ Pires tandem trigger regular tertiary structures, exactly by a Idiart, Instituto de F´ısica plurality of different sizes and functions resulting in diffe- Universidade Federal do Rio Grande do Sul In the ENFE - 04/11/2015 - Abstracts 61 search of understanding how the brain processes the [3] S. D. da Cunha, R. R. Vidigal, L. R. da Silva, and R. position and navigation of an animal, researchers found Dickman, Eur. Phys. B 72, 441 (2009). cells in the hippocampal region that were tuned to posi- [4] S. D. da Cunha, L. R. da Silva, G. M. Viswanathan, tions in space. The first type of cell to be characterized and R. Dickman, J. Stat. Mech. (2014), P08003 (2014). in the 70s were the place cells, pyramidal cells that are [5] M. Basu, U. Basu, S. Bondyopadhyay, P. K. Mohanty, active when the animal is in a particular position in the and H. Hinrichsen, Phys. Rev. Lett. 109, 015702 (2012). environment. In 2005 researchers found a yet more intri- [6] S. B. Lee, Phys. Rev. Lett. 110, 159601 (2013). guing type of cells in an adjacent area called entorhinal [7] S. B. Lee, Phys. Rev. E 89, 060101; 062133 (2014). cortex, the grid cells. When a rat moves in 2D space, the [8] J. J. Ramasco, M. A. Mu˜noz, and C. A. da Silva San- grid cells fire action potentials according to a hexagonal tos, Phys. Rev. E 69, 045105(R) (2004). pattern, covering the environment with a grid of activity. Our study focus on the understanding of a continuous [04/11/2015 - P012] attractor model of grid cells proposed by Burak & Fiete Vorticity Curvature Criterion for Two- (2009). In the model the activity in the network is Dimensional Vortex Identification, linked to the rat’s translation, so that change of position Jose´ Hugo Capella Gaspar Elsas, Luca Ro- of the rat creates a corresponding displacement of a berto Augusto Moriconi, Insituto de F´ısica - group of centers of activity in the network. In our study Universidade Federal do Rio de Janeiro Vortical we focus on the boundary properties of the network. structures are an emblematic feature of turbulent flow, Periodic networks integrate better the position compared and, recently, due to better experimental techniques and to aperiodic networks. However periodic networks may computer simulations there is a growing interest in vorti- present stable pattern of activities with grid defects and cal, and, more generally, coherent structures in turblent in discrete orientations, while aperiodic networks are fluid flow[1]. Systematic procedures for the identification more flexible in orientation and do not present defects. of vortices/coherent structures have been proposed as a We also study how the propensity for grid defects of way to address their kinematical and dynamical roles in periodic networks depends on the model parameters. structural formulations of turbulence[2]. As a general rule, all of the known vortex detection algorithms are plagued with shortcomings[3]. In this work, we focus COMPLEXITY & INTERDISCIPLI- on one of the most popular methods - the swirling NARY TOPICS strength criterion - and investigate how it performs in controled Monte-Carlo tests. We, then, emphasize its [04/11/2015 - P011] main problematic issues: (i) vortex deformation and Diffusion, correlations and mobility in a two- suppression due to the near presence of intense vortical dimensional conserved stochastic sandpile, structures; (ii) vortex merging; (iii) spuriuos vortices Sharon Dantas da Cunha, UFRN/UFMG, Ronald created in many-vortex configurations and (iv) in the Dickman, UFMG The conserved stochastic sandpile presence of background shear. The inner layer of tur- (CSS) belong to a universality class called conserved bulent boundary layer flows is, in particular, the region directed percolation (CDP) [1,2,3,4], distinct from direc- where the swirling strength criterion looses accuracy ted percolation (DP). The existence of the CDP class in a dramatic way. We propose an alternative vortex was nevertheless questioned by Basu et al. [5], who detection criterion, based on the curvature properties claim that the one-dimensional CSS belongs to the DP of the vorticity profile, which clearly improves over the class, but these results were reexamined in one and results obtained with the swirling strength criterion in a two dimensions by Lee [6,7], who presented numerical number of relevant case studies. evidence to prove the existence of CDP. In this work Bibliography: we perform large-scale simulations of a two-dimensional [1] D. Dennis, Anais da Academia Brasileira de Ciˆencias restricted-height conserved stochastic sandpile, focusing 2015 [2] Moriconi, L., Phys. Rev. E 79/4, 2009 [3] Jeffrey on particle diffusion, spatial correlations and mobility. A. LeHew et al., Caltech Ph.D thesis, 2012 Initially we use Quasistationary simulations (QS) to de- termine the critical particle density [pc = 0.7112687(2)], [04/11/2015 - P013] and show that the diffusion constant scales in the same Degree distribution orients the flux of manner as the activity density, as found previously in information in network of networks, the one-dimensional case [3]. We analyze the particles Mariana Sacrini Ayres Ferraz, Alexandre mean-square displacement (msd) and verify the subdiffu- Hiroaki Kihara, Laborat´orio de Neurogen´etica, sive behavior in the initial (“short-time”) scaling regime, UFABC Neuronal networks oscillate across a broad and linear, in the stationary regime. At criticality, the range of frequencies, leading to synchronization to be a β/ν activity correlation function behaves as C(r) r− ⊥ . very intriguing subject in both neuroscience and dyna- Our results for critical exponents are consistent∼ with mical systems. A large number of physiological functions predictions derived from the Langevin equation for sto- depend on the coordination of neurons, which act in chastic sandpile in two dimensions [8]. The effect of weak concert, generating specific rhythm in certain regions force or bias f were studied in CSS, where we implement of the brain. These several synchronous rhythms are the bias by altering the transition probabilities and the resulted from properties of individual neurons, plasticity results were consistent with theoretical relationships. of synaptic coupling, as well as the network topology. [1] R. Dickman, Phys. Rev. E 73, 036131 (2006). It is expected that neuronal networks on the brain [2] J. A. Bonachela, M. A. Mu˜noz, Phys. Rev. E 78, operate on criticality, showing advantages in information 041102 (2008). processing and pattern formation, which maximize the 62 Abstracts - ENFE - 04/11/2015 numbers of metastable states. Also, the topology is said great effort because we are facing a complex system. In to be like scale-free, predicting the existence of hubs this work, we assess the scale properties of changes in that correspond to highly connected neurons. Circuitries share prices of seven oil companies listed in the NYSE from different regions are interconnected, thus the stock market between the years 2008-2015 by using frac- brain can be considered as a network of networks. In tals properties. In order to do that we use the method this context, very little is known about how different Detrended Fluctuation Analysis (DFA), that through a networks synchronize themselves. In this work, we used power-law relation between its detrended function and random and scale-free networks, according to Watts- α coefficient of correlation shows self-affinity properties Strogatz and Barab´asi-Albert models. Both networks in non-stationary time series. In additional we quantify were connected by highly connected nodes and hubs, the cross correlation among all seven companies by respectively. We used leaky integrated-and-fire (IF) using the Detrended Cross correlation Analysis (DCCA) neuron model to simulate plausible neuronal network method, that is based on DFA. The results showed activity. Surprisingly, our results indicated that random anti-persistent DFA α coefficient for all seven companies networks have more influence in the synchronization of and the DCCA λ coefficients were correlated among all scale-free networks than the other way around. However, time series. Furthermore, we use these two methods this tendency can be neutralized and even reverted combined in order to present statistical evidence that with the monotonic increase of the networks oscillatory prices oil companies variation are consistent with the frequency. Therefore, we were able to provide formal Efficient Market Hypothesis (EMH). Supplementary, demonstration that a system of networks can self-govern the α coefficient and λ coefficient show that individual the flux of information over its parts. In summary, oil company motion cannot be predicted on long range, we demonstrated for the first time that information unless that a trader analyze the behavior motion of all directionality can be “embedded”into the networks, companies, that avoid that individual disturb or some providing new possibilities for system designing, as speculation action affect the its scale properties. The possibly observed in interconnected cerebral areas with main contribution of this paper is present these scale distinct degree distribution. methods (DFA and DCCA) working together in favor to [04/11/2015 - P014] help purchases and sales assets. Fractal aspects in O2 enriched combustion, [04/11/2015 - P016] Jefferson W. G. de Souza, Alex Alisson B. San- Impact of the network structure on plurality rule tos, Lilian Lefol N. Guarieiro, Marcelo A. Mo- opinion dynamics, Vivian Dornelas, Celia An- ret, SENAI - Cimatec The study of the technology of teneodo, Depto. de Fisica, PUC-Rio People often flame enrichment with oxygen, together with the study face the challenge of choosing amongst different options of soot formation coupled with thermal radiation, has with similar attractiveness, such as when choosing a par- attracted interest in industries that involve combustion lamentary candidate, a movie or buying a product in the processes where a large amount of energy is released as supermarket. In order to study the distribution of pre- heat and, consequently, light. The main objective of com- ferences in such situations, it is adequate to consider a bustion is maximize the heat while minimizing the pro- plurality rule opinion dynamics on small-world networks, duction of polluting gases. The more harmonic the union where different options are available as well as the un- of these elements, the more efficient the combustion will decided state. Depending on the structural properties be. The stoichiometry of the fuel composition provides of the network and on the initial conditions, the final a basis to calculate the required amount to be burnt in distribution can range from a wide distribution of prefe- the reaction. Although there are existing studies on the rences to consensus, or also give rise to situations where mechanisms of soot formation and control, a more de- indecision dominates. Decision making governed by the tailed understanding of these processes is important for plurality rule may yield ties, contributing to overchoice technological advances in environmental impact (emis- stagnation. This is more pronounced in random networks sion of polluting gases). In this study, we investigate than in scale-free ones. Also, in the latter networks con- the self-affinity of time series of thermal radiation from sensus is facilitated. However, it is not still clear which two fuels, natural gas (NG) and acetylene (AC), enriched are the contributions of randomness and preferential at- with oxygen at 21%, 23% and 25% concentrations during tachment for those effects. In order to investigate that the combustion process. We used the detrended fluctua- issue, we develop the plurality rule dynamics in gene- tion analysis method to evaluate the burning process of ralized Watts-Strogatz networks. We start from regular these fuels. We found a well-defined self-affine aspect for networks and rewire their connections to obtain different these gases in this dynamic process. Using the proposed degrees of randomicity p. Moreover, the rewired nodes method, we were able to characterize the time series of can be selected by means of a parameter w which allows NG as a sub-diffusive process and the time series of AC to tune from random selection to preferential attachment. as a process with persistent self-affinity. Through a phase diagram in (p, w) space, we characterize [04/11/2015 - P015] the conditions that lead to the different final configurati- Oil Companies Share Prices Self-Affinity, ons. Jefferson Willes G. de Souza, Alo´ısio S. Nasci- [04/11/2015 - P017] mento Filho, Marcelo A. Moret, SENAI - Cimatec Self-affinity and dengue fever, The study of the variation of share prices on the stock Stela M. Azevedo, Universidade Estadual de Feira market, as well as their behavior in the long range are de Santana, Hugo Saba, Universidade do Estado not an easy task. Indeed the attempt to understand the da Bahia, Jose´ Garcia Vivas Miranda, Universi- underlying behavior on financial normally it requires a dade Federal da Bahia, Aloisio Nascimento Filho, ENFE - 04/11/2015 - Abstracts 63 Marcelo A. Moret, Faculdade de Tecnologia SENAI order parameter reveal an unexpected behavior not de- CIMATEC Dengue is a complex public health problem tected by the well-established order parameters. In some common in tropical and subtropical regions. This disease cases, the maximum cohesion does not occurs for trivial has risen substantially in the last three decades and the values of noise and interaction radius. physical means depicts the self-affine behavior of the [04/11/2015 - P019] occurrences of reported cases of dengue in the state of A Monte Carlo Study of Entropy from Bahia-Brazil. This study uses Detrended Fluctuation Sound Spectra, Debora Coimbra Martins, Analysis (DFA) to verify the scale behavior in time series Joao˜ Lucas de Paula Batista, Universidade Federal of cases of dengue and to evaluate the long-range corre- de Uberlˆandia Percussion instruments are impulsively lations characterized by the power-law α exponent for excited instruments which would work even if their different cities of the state of Bahia-Brazil. The scaling behavior were strictly linear. They are classified as exponent (α) presents different long-range correlations, “incidentally nonlinear”because, at small excitation i.e., uncorrelated, anti-persistent, persistent and diffusive amplitudes, their sound output is based entirely upon behaviors. The long-range correlations highlighted a their natural mode frequencies, despite the fact that complex behavior of the time series of this disease. nonlinearity sometimes contributes a great deal to their The findings show that there are two distinct kinds of sound. In this work, we studied Shannon entropy of scale behavior. The first one, the time series presents suitably preprocessed Fourier spectra obtained from a persistent α exponent for a period of one month. cuica 8 inches (a brazilian percussion instrument) by Nevertheless, for large periods, the time series signal Monte Carlo method. First the sound is recorded using approaches of the subdiffusive behavior. The hypothesis a professional microphone and decoded in WAV format of the long-range correlations in the time series of the through Audacity software. We implemented Fast occurrences of reported cases of dengue was validated. Fourier transform aplaying MatLab R package to obtain The observed self-affinity can be useful as forecasting indexed frequencies spectra. We found fundamental tool in future periods through an extrapolation of the α frequencies 661 Hz (E5) to sharp and 347 Hz (F) to exponent behavior. This complex system has a higher bass sound. To each coarse-grain clustered in a subset predictability in relatively short time (about one month) of harmonics, the power spectrum was binned defining and it suggests a new tool in epidemiological control an array, corresponding to a suitable frequency. In this strategy. However, predictions for large periods using representation, adjacent bins differ by a frequency ratio DFA are hidden by the subdiffusive behavior. of one cent. We mapped the correspondends intensities and computed Shanon entropy. We change randomly [04/11/2015 - P018] Diagnostic of spatial organization in the Vicsek one of pitches and compute the entropy again. If entropy Model, Tiago Kroetz, Gabriel Sousa, UTFPR obtained is lower the change is accept, otherwise restore the previous value. The procedure is iterated until Collective motion is the name given to the complex behavior exhibited by a set of moving elements interac- no further improvement restore previous value. This ting with each other. The moving elements are usually procedure furnish local minimum of the entropy and called “self-propelled particles” and normally represent is inherently sensitive to all frequencies intervals. The living organisms with some kind of simple interaction ru- authors thank FAPEMIG by financial support. les with their neighbors. Schooling, swarming, herding and flocking are examples of a wide variety of collective COMPLEXITY & INTERDISCIPLI- behaviors exhibited by groups of animals, insects or bac- NARY TOPICS teria. The interest on models of self-propelled particle is to understand how and why individuals become unified [04/11/2015 - P020] groups. We propose a method to measure the cohesion Modelling the Air-Water Interface, of collective motion exhibited by self-propelled particles Frank Longford, University of Southampton, and compare to the already existent methods. We per- Institute of Complex Systems Simulation, Jonathan form this study using the well-known Vicsek model. In Essex, Chris-Kriton Skylaris, Jeremy Frey, Uni- this model, all the elements move with a constant ab- versity of Southampton, School of Chemistry Water solute velocity and at each time step they assume the is an incredibly important molecule for chemical and average direction of their neighbors into a chosen radial biochemical modelling of complex systems. Despite distance. A random angle is added to the average di- this, many of its emergent properties are not fully rection of each element, which are considered to be a understood. Recent ellipsometry experiments into natural perturbation caused by the many stochastic and probing the surface of water-air interface have shown deterministic factors affecting the motion of the living or- the presence of a water-like surface film with a much ganisms. The most common diagnostic for measure the higher refractive index of light than the bulk solvent [1]. self-organization of the system is the average normali- This runs counter to molecular dynamics calculations, zed vectorial velocity. This order parameter is capable to which propose a tapering off of molecular density in quantify the directional organization took by the particles this region over sub-nm thickness, and of refractive but omits the spatial distribution of the set. We intro- index as well. It has been suggested that there is some duce an order parameter based on Informational Entropy emergent behaviour of water molecules at the air-water defined by Claude Shannon applied separately on the po- interface that give rise to the high electric field at the sitions and directions distributions. This method gives surface, causing the observed higher refractive index. a normalized quantification of spatial and directional or- Ellipsometry experiments can be simulated by studying ganization of the system. The results obtained by this the arrangement of molecules at an interface during a 64 Abstracts - ENFE - 04/11/2015 molecular dynamics (MD) simulation in terms of order fact strongly suggests that these astrophysical systems parameters to calculate surface polarisation. Usually behave in a nonextensive manner. Furthermore, the q hyperpolarisabilities are then taken from quantum simu- entropic indices for these systems were obtained and they lations to describe the molecular response to an applied provide an indication of the nonextensivity degree of each electric field, however these are normally parametrised of these astrophysical systems. The q-value increases for to a single molecule and so may neglect complex surface systems if the Tsallis entropy decreases. interactions. In addition, performing quantum MD [04/11/2015 - P022] simulations on large scale systems to simulate physical Wavelet-based entropy: a new ap- experiments is highly time consuming, so a full ensemble proach for characterizing time series, of states may not be generated within the computational Marcos Vin´ıcius Candidoˆ Henriques, Marcos resources available. Therefore, it is advantageous to Vin´ıcius Cˆandido Henriques, Francisco Edcarlos perform as much of the simulation as possible using Alves Leite, Universidade Federal Rural do Semi- classical polarisable force field methods. Using the Arido´ , Liacir dos Santos Lucena, Universidade commercially available AMBER 12 molecular mechanics Federal do Rio Grande do Norte Quantitatively software we have so far implemented ways to deal with characterizing the degree of order-disorder in finite reso- long range Lennard-Jones force corrections based on the lution multi-frequency time series is a major challenge methodology of Janeˇcek [2]. These corrections to particle due to limitations imposed by mensuration scales. The forces and energies can be accurately dealt with during Wavelet transform is a multiresolution mathematical post-processing in systems containing homogeneous tool that allows one to decompose a signal into mul- densities, but it becomes necessary to include them tiple components, each one representing some scale of “on-the-fly” during each simulation time-step in the observation. We apply the Tavares-Lucena Wavelet presence of interfaces. We present an overview of how Entropy (TLWS), which is based on the discrete wavelet these force corrections are important for replicating transform, to analyze an ensemble of Gaussian stochastic surface behaviour in Lennard-Jones fluids, and also processes following Fractional Brownian Motion (FBM), the development of a novel way to thermodynamically generated from different methods and with distinct estimate surface energetic and entropic terms to assess Hurst exponents. In order to test the reliability of their accuracy. this new method, we compare the results for entropies [1] R. Greef, J.G. Frey; The Water-like Film on Water, with those obtained by using the traditional Shannon Phys. Stat. Sol.; 5, 1184 (2008) entropy. In an attempt to measure the balance of [2] J. Janeˇcek; Long Range Corrections in Inhomogeneous order-disorder of multi-frequency stochastic signals that Simulations, J. Phys. Chem. B; 110, 6264 (2006) can be modeled as Gaussian process, we apply TLWS [04/11/2015 - P021] formalism to analyze the statistical properties of time Non-additive complex systems: Applications series of financial data (BOVESPA) in different periods. in Astrophysics, Chemistry and Engineering, We show that the wavelet-based entropy measure can be Antonio C. do P. Rosa Jr., UFOB - BA - Brasil, a good characterization method for stochastic processes Pablo Vaveliuk, CICBA-CONICET - La Plata - Ar- as those used for modelling financial data. It allows gentina, Marcelo A. Moret, SENAI-CIMATEC - BA to distinguish periods related to different degrees of - Brasil In this work, a physical modeling for the sto- volatility, besides dealing well with the presence of noise, chastic dynamics based on nonlinear continuity equations which can be easily eliminated with a suitable choice of is proposed. In this sense, self-similarity, long range cor- scales. relations, self-organized criticality, among others, occurs [04/11/2015 - P023] in complex systems. Besides, non-Markovian stochastic Using the Theory of Social and Complex processes might be noticed. The probability densities are Networks for Applying Business Logistics Solu- solutions of the nonlinear Fokker-Planck equations that tions, Carlos Cesar´ Ribeiro, Marcelo A. Mo- maximize the non-additive Tsallis entropy. Based on a ret, Hernane B. B. Pereira, SENAI CIMATEC nonlinear Fokker-Planck equation, a diffusion coefficient Modern society increasingly demand speed and quality that it is proportional to the supercooled-liquid concen- of the logistics industry in its operations, forcing them to tration is observed. The proposed model allows explai- seek innovative alternatives that make them competitive. ning the anomalous behavior of the diffusivity. We de- To Fawcett& Clinton (1996) modern companies are at a monstrate that this new approach is consistent with ex- time of developing new production philosophies, growing perimental patterns. Besides, it could be applied to non- global competition, supply chain development and a great Arrhenius chemical kinetics. Then, a reaction-diffusion emphasis on the use of information technology. In this model to non-Arrhenius chemical kinetics is proposed. sense, the use of Social and complex networks theory has On the other hand, this non-Markovian model properly become one of the main methods used by logistics ma- depicts the time evolution of a distribution of depth va- nagers in the search for solutions that result efficiency lues of pits that were experimentally obtained. The so- and competitiveness in its processes. Importantly, the lution of this equation in a steady-state regime is a q- analysis of social networks and Complex is defined as the Gaussian distribution, i.e. a long-tail probability distri- mapping and investigation of the relationship between bution. In additional, the X-ray intensities of 142 light a particular group of actors (Scott, 2000). Relations, curves of cataclysmic variables, galaxies, pulsars, super- specifically in logistics, can be constructed and applied nova remnants and other X-ray sources are studied. The in the most important modal, as a transport of goods X-ray light curves coming from astrophysical systems from one city to another (road transport), from port to obey q-Gaussian distribution as probability density. This port (water modal) and between one airport to another ENFE - 04/11/2015 - Abstracts 65 (modal air transportation). Such relationships, network distributions. For the present paper the research tasks theory, are built from the identification of vertices (focal analyzed 136 curves relating to time series evolution of points such as ports) and edges (transport of goods) that X-Ray emission values of XRBS. Some nonlinear Fokker- when applied in specific softwares such as Pajek or UCI- Planck equations present as solution to the steady-states NET result in a series of strategic indicators that provide q-Gaussian distributions. We recall that it was in good the logistics manager taken more assertive and competi- accordance to the data provided by the X-Ray Rossi sa- tive decisions. Using the theory of Social Networks and tellite. The results showed accuracy with respect to the Complex in logistics organizations allow administrators original data, by means of analysis of variance (ANOVA), to better manage their supplier relationships, determine with FV alue = 140297 and P rob > F = 0. In all analy- assertive decisions on physical distribution and also get zes the q-Gaussian distribution proved better fit to the cost savings throughout the supply chain (Supply Chain). points regarding the Gaussian distribution, demonstra- In conclusion, Social Networks and Complex focus in re- ting the non-extensive character of the behavior of the lations between actors as the main unit of analysis, and X-Rays emissions arising from XRBS. such relationships may result in management information [04/11/2015 - P026] capable of providing organizations, efficiency and effecti- Complex Features in a Network of Worldwide veness in their logistics processes. Seismic Events, Bernardo A. Machado, Paulo S. [04/11/2015 - P024] L. Oliveira Junior, Douglas S. R. Ferreira, LIS- WORLD CUP 2014 - AN ANALYSIS OF Comp, IFRJ - Campus Paracambi The understanding THE PERFORMANCE OF PLAYERS, of long-distance relations between seismic activities has Antonioˆ J. A. Cordeiro, SENAI CIMATEC e for long been of interest to seismologists and geologists. ESTACIO´ , Hernane B.B. Pereira, Marcelo A. Despite all the existing knowledge about the production Moret, SENAI CIMATEC e UNEB Since 1930, of seismic waves through slips on faults, much remains when the first football world championship was lunched to be discovered regarding the dynamics responsible for it has increasingly attracted the audience and the teams these slips. A key step in deepening this knowledge is from different countries made this event a great success the study, analysis and modeling of the seismic distri- of public in additional an important bussiness. Each butions in space and time. In this paper we have used four years one of the biggest expectations is the choice data from the world-wide earthquake catalog for the pe- of selecting the best players of the competition, which riod between 1972 and 2011, to generate a network of it takes into account a set of subjective information, sites around the world for earthquakes with magnitude originating from the observation of the games thus such m 4.5 in the Richter scale. After the network construc- choices become subject to disputes as to the actual tion,≥ we have analyzed the results under two viewpoints. performance and contribution of each player to the Firstly, in contrast to previous works, which have consi- team’s success during the competition. One of the main dered just small areas, we showed that the best fitting difficulties to meet these challenges is the ability to for networks of seismic events is not a pure power law, consider statistical data of the players in each game, but a power law with exponential cutoff. We also have such as right and wrong passes, assists that generated found that the global network presents small-world pro- submissions, tackles, crosses and more. In this work, perties. Secondly, we have found that the time intervals seeking to fill that gap, multivariate statistical analyzes between successive earthquakes have a cumulative proba- are presented: Cluster Analysis, Faces of Chernoff, bility distribution well fitted by nontraditional functional K-means, multidimensional scaling, based on data collec- forms. Our results reinforce the idea that the Earth is in tion matches of the FIFA 2014 World Cup held in Brazil. a critical state and furthermore point towards temporal The results can be useful for analyzing the choices of and spatial correlations between earthquakes in different the best athletes in a competition, identifying players places. We also sketch some future trends of our work. clusters with similar characteristics game, discovery of patterns of play to assist in the decision-making process NON-EQUILIBRIUM by the football coach. [04/11/2015 - P025] [04/11/2015 - P028] Non-extensivity of the X-ray binary systems, Synchronization of a computationally efficient Melina Silva de Lima, Marcelo A. Moret, SE- neuron model with memory and synaptic delay, NAI/CIMATEC Systems in stationary states or in Germano S. Bortolotto, Mateus Kinasz, Mar- quasi-stationary states that cannot be consistently ap- celo H. R. Tragtenberg, Departamento de F´ısica, proached by classical Boltzmann and Gibbs Thermos- Universidade Federal de Santa Catarina Experiments tatistics are non-additive. On the other hand, objects have recently shown synchronization in pairs of biological whose gravitational forces display a long-range gravitati- neurons. Several models have been studied, from biolo- onal reach are parts of so-called Self-Gravitating Systems gical plausible ones like the Hodgkin-Huxley model to (SGS). For both cases, the Generalized Thermostatisti- formal models (Rulkov). We use the modified Kinouchi- cal formalism (GTS) proposed by Tsallis is a possible Tragtenberg (KTz) model to study the synchronization tool to be applied in replacement of classical Thermos- of two coupled identical neurons with memory and synap- tatistics. X-Ray Binary Systems (XRBS) are SGS ob- tic delay. The KTz is a logistic neuron model with the jects that present quasi-stationary states features. If one membrane potential described by the discrete time recur- knows their emission values of light curves it is possible sion relation x(t +1) = f(u(t)), where f is a sigmoidal measuring their probability density distributions. The function, u(t) = [x(t) Ky(t)+ z(t)+ I(t)]/T , I(t) is an obtained results presented as the best fitting q-Gaussian external current and z−(t) is a slow current. We study the 66 Abstracts - ENFE - 04/11/2015 case where f(u)= u/[1 + u ]. This is a computationally contact, when compared to the expectations for regular efficient neuron model with| | many dynamical behaviors lattices. With many practical applications, the case similar to biological neurons: excitable fixed point, fast of epidemic models on heterogeneous social contact and slow regular spiking, bursts and spikes with plateau networks is particularly important in this respect. In etc. Using a master-slave configuration we demonstrate scale-free networks, with degree distribution exhibi- γ that depending on the relationship between memory and ting long tails of the form P (k) k− , the epidemic synaptic delay times the neurons synchronize either with threshold can vanish in certain models.∼ Therefore, a anticipation or with lag. We use the similarity function disease can spread macroscopically, irrespective of its S2(φ) to characterize anticipation and lag. The difference infective rate. There is an ongoing scientific debate between memory and synaptic delay times corresponds regarding the nature of this null threshold, concerning to the mean delay time. We vary the coupling strength its origin in the simplest susceptible-infected-susceptible between two neurons in order to show that it controls (SIS) model. A more realistic epidemic model is the phase-locking and frequency entrainment of the system. susceptible-infected-removed-susceptible (SIRS), which considers immunization or death for the dynamics. [04/11/2015 - P029] In this process, an infected node turns to a removed Sampling methods for absorbing-state phase tran- state during an averaging time 1/α, before becoming sitions on complex networks, Renan S. Sander, susceptible again. In this work, we show analytically, and Silvio C. Ferreira, Universidade Federal de Vi¸cosa verify numerically (using quasi-stationary simulations Phase transitions into absorbing states, configurations on degree-uncorrelated power-law networks) that the from which the system cannot escape, are a current topic dynamics on hubs (basically large star graphs) plays an on the frontier of the non-equilibrium statistical mecha- important role for general epidemic processes on top nics. Despite the fact that there are still problems being of networks. Our non-mean-field theoretical analysis investigated on regular topologies, phase transitions on is based on the interplay between lifetime of hubs and complex networks have been subject of increasing inte- the reinfection mechanism presented in the SIRS model rest to the scientific community due to the fact that such and leads to different predictions, based on the value networks describe a wide variety of systems, relevant both of the degree exponent γ. We analyzed numerically the in the technological and intellectual aspects. Conside- density of infected vertices, the epidemic lifespan and a ring the dynamical nature and huge size of real complex susceptibility definition that presents a divergence at the networks, the statistical physics approach has proved to transition point to an endemic phase. For networks with be suitable since its association with the graph theory γ < 3, we found a vanishing threshold in the infinite-size permits a characterization of emergent macroscopic phe- limit, as observed in the SIS model. For γ > 3 our nomena in terms of the time evolution of basic elements simulation results shows a threshold that converges composing the system. Since numerically we deal with to a finite value for not large values of α, contrasting finite systems necessarily, and finite-size effects are parti- with the vanishing threshold of the SIS model. These cularly stronger on power-law complex networks than on results are backed up by our theoretical formulation. its regular lattice counterparts, a finite-size scaling (FSS) Acknowledgement: FAPEMIG analysis is required. In this work, we perform simula- tions for the susceptible-infected-susceptible (SIS) model [04/11/2015 - P031] and the contact process (CP) on power-law networks with Analysing the reinfection effect for transmitted γ a degree distribution P (k) k− , using three different diseases and social adoptions through stochasti- sampling techniques: the reflecting∼ boundary condition cal SIRI model, Alessandro de Barros, Instituto (RB), the coupled vanishing external field (EF) and the Federal da Bahia, Lucas Tinti, Roberto Andrade, quasi-stationary (QS) simulation methods. We show that Suani Pinho, Universidade Federal da Bahia, Jesus the three methods are equivalent for the CP, successfully Gomes-Gardenes, University of Zaragoza The rein- capturing its critical behavior on networks. The SIS on fection effect is relevant for many transmitted diseases power-law networks presents multiple transitions and for such as Tuberculosis and Viral Hepatitis. In such cases, this model the three sampling techniques successfully cha- the second infection is less probable than the primary racterize the transition associated to an endemic phase one. On the contrary, in social context, in general, the (diverging lifespan), but provide different results for tran- primary adoption of a product, innovation or idea is less sitions involving localized states. In this regime, the RB probable than the second one [1]. For both cases, an and EF method do not capture, for example, a transi- stochastic version of the SIRI model is able to translate tion associated with the activation of the most connec- the spreading idea, based on the following compartments: ted vertex of the network, as predicted by the quenched Susceptible (Ignorant), Infected (Spreader) and Recove- mean-field theory (QMF). Acknowledgement: FAPEMIG red (Inactive). The dynamical rules between compart- ments are given by: S + I 2I with infection rate β; → [04/11/2015 - P030] I R with recovery rate γ; R + I 2I with reinfection Epidemic thresholds of the susceptible-infected- rate→ σβ. When σ = 0, the stochastical→ SIR model is re- removed-susceptible process on networks, covered. We set up the master equation for stochastical Renan S. Sander, Silvio C. Ferreira, Universidade SIRI model. According to one-site and pair mean-field Federal de Vi¸cosa, Romualdo Pastor-Satorras, approximations of the master equation of SIRI model on Universitat Polit`ecnica de Catalunya Heterogeneous a lattice, for σ < 1, the relevant scenario for transmited topologies, as observed in many natural and artifi- diseases, there is a phase transition between the endemic cial complex networks, can fully alter the behavior and epidemic states. For σ < 1 , Monte Carlo simulati- of dynamical processes mediated by such patterns of ons also exhibit a second-order phase transition between ENFE - 04/11/2015 - Abstracts 67 endemic and epidemic phases, revealing that SIRI model C3ν symmetry, Oscar A. Barbosa, Taniaˆ Tome´ is in the same universality class of directed percolation. Martins de Castro, USP - SP - Brasil Lattice non However, for σ < 1, the relevant scenario for social adop- reversible models characterized by the own symmetry of tions, the phase transition becomes abrupt in a network. the imposed dynamics are dealt. The dynamics is con- We are studying analitically the stochastical SIRI mo- sidered Markovian and stochastic, ruling the time evolu- del in homogeneous and heterogeneous networks in order tion of the system by means of the master equation, that to investigate the effect of the connectivity distribution determines in time the configuration space. The work on the phase transition as it was previously done for the is focused on the study of the critical behavior of the stochastical SIS model [2]. entropy production, as this physical quantity shows to [1] J. G´omes-Garde˜nes, A. S. De Barros, S. T. R. Pinho, be susceptible to the irreversibility of the system from its R. F. S. Andrade. Abrupt transitions from reinfections own definition, but also because its construction comes to in social contagions. EPL 110, 58006 (2015). be coherent with a treatment of the model which takes [2] R.S. Sander. Transi¸c˜oes de Fase para Estados Absor- into account the contributions done by the its basic com- ventes: um estudo em redes regulares e complexas. Dis- ponents, hence, supplying a perspective which explains serta¸c˜ao de Mestrado: Universidade Federal de Vi¸cosa, the global behavior of the system as a consequence of the Brasil (2011). considerations done on its basis. Being so, it’s proposed a three state Potts model on a [04/11/2015 - P032] A Stochastic Differential Equation Approach square lattice which is ruled by an irreversible dynamics to Spectral Fluctuations in systems with Mi- with symmetry properties in the C3ν group. For the en- xed Dynamics, Ivan´ Gonzalez´ , Antonioˆ M S tropy production it’s chosen the Schnakenberg prescrip- Macedo,ˆ UNIVERSIDADE FEDERAL DE PERNAM- tion, being harmonic with a Markovian stochastic pers- pective which is supposed to act in a microscopical le- BUCO The distribution of energy level spacing in mi- xed ballistic cavities (where regular and chaotic dynamics vel, as stated. Using Monte Carlo simulation its critical may coexist), can be understood in terms of a Wigner- properties are analyzed, characterizing the expected di- Dyson distribution with fluctuating variance σ2. Ina vergent tendency of its derivative at the critical point. recent work [1-4], a detailed analysis of the spacing dis- Other quantities as the order parameter are calculated, tribution in mixed cavities was made using the method of since these allows a complete description of the system statistic superposition (or superstatistics). It was found response to the control parameter, and elucidates fea- that σ2 is well described by a chi square distribution, tures as the phase transition, its nature, and also the which in turn is used to obtain the corresponding spacing properties of the states involved in each of the phases. distribution via Bayes theorem. Another interesting re- Dynamics and stationary critical exponents are calcula- sult is the estimation of the time scales in the problem via ted from the numerical results, those being a signature of the time correlation function for the spacing S, yielding the universality class of the system, which, in accordance to the Grinstein conjecture, shouldn’t depend on the re- two time scales τ1 and τ2, and the kurtosis of the spacing distribution, yielding the time scale T . The estimated versible conditions, but just on the symmetries involved T turned out to be one order of magnitude larger than in the model, as most of our results confirm. τi, which was used to justify the superstatistical method [04/11/2015 - P034] for deriving the spacing distribution. However, no model From quasi-stationary states to multi- description was given for the time correlation function absorbing states growth model., of S [3]. Furthermore, the time correlation function of DIEGO ALEJANDRO CARVAJAL JARA, FRAN- σ2, which could yield additional large time scales [4], was CISCO CASTILHO ALCARAZ, Instituto de f´ısica not studied. In this work, we describe the fluctuations of de S˜ao Carlos - USP A one-dimensional growth energy spacing levels in ballistic quantum cavities with model with local absorption and nonlocal desorption mixed dynamics using a coupled system of stochastic dif- is studied. Its phase diagram is characterized by two ferential equations (SDE). The main advantage of our parameters, one controlling the temporal correlation and method is the possibility to account for all time scales of the other describing the ratio between the absorbing the problem, thus describing in the same dynamical mo- and desorbing rates. Depending on the parameters, the del both the spacing distribution and its time correlation stochastic model exhibits either self-organized criticality, function. The results of the superstatistical method are quasi-stationarity, multi-absorbing transitions or massive recovered in the limit where all time scales ratios go to behaviors. Two boundaries are of special interest: the infinity. Our SDE model is an extension of recent gene- first separates the region with self-organized criticality ralization of statistical ensembles to multiscale systems, from the one of massive behavior, and it corresponds to in which an Ornstein-Uhlenbeck inverse gamma (OUIG) a conformal invariant growth model. The second divides process with M time scales is coupled to a single vari- the regions of quasi-stationarity and of multi-absorption able Langevin equation with one time-scale [5]. In our phase and it appears as a critical line in the phase model we couple Dysons random matrix process with N diagram. time-scales to an OUIG process with M time-scales. A In the non-equilibrium regime, we observe quasi- detailed analysis of some particular cases (N = 2, M = 1) stationary states with an exponential increase in the li- and (N = 2, M = 2) is provided and both the spacing fetime as a function of the size system, a behavior typi- distribution and the time correlation functions are calcu- cal of activated dynamical scaling. In the no-absorption lated from the same model. case, the dynamics of the surface can be derived analy- [04/11/2015 - P033] tically and exhibits a transient dynamic whose timescale Entropy production for irreversible systems with is much larger than the expected lifetime of 1/E1, with 68 Abstracts - ENFE - 04/11/2015 E1 the energy gap. This timescale behaves like a ”critical less relaxation. The stationary collisionless Boltzmann initial slip”and strongly depends on the size of the big- (Vlasov) equation with appropriate boundary conditions gest cluster in the initial condition. This highlights the is reduced to an ordinary differential equation, which is need of controlling the typical size of the clusters in the then solved numerically. Special attention is given to the initial conditions, otherwise the estimation of dynamical space-charge limited transition when the electron density exponents may be erroneous. becomes high enough to screen the accelerating electric Finally, we observe deviations from the conformal tower field at the cathode. It is found that while for unmag- in the no-absorption case when investigating the criti- netized diodes this transition is always continuous [1], in cal transition from the absorbing to the multi-absorbing the case of crossed-field diodes it becomes discontinuous phase, as an additional parameter in the model in tuned. below a critical temperature [2]. We also investigate how [04/11/2015 - P035] intrinsic space-charge oscillations may drive stationary Phase Transitions in a Non-equilibrium System states unstable in certain parameter regimes [2]. The re- with Parity Conservation and Long-range Dif- sults are verified with molecular-dynamics simulations. fusion, Taina˜ L. M. Silva, Marcelo Leite Lyra, [1] F. B. Rizzato, R. Pakter, and Y. Levin, Phys. Rev. UFAL - AL - Brasil, Carlos Argolo, IFAL - AL - Bra- E, 80, 021109 (2009). sil The Contact process is the simplest model for phase [2] S. Marini, F. B. Rizzato, and R. Pakter, Phys. Plas- transitions out-equilibrium and it was originally introdu- mas, 21 083111 (2014). ced to describe epidemic spreading models. In the present work, we study the effect of long-range interactions pro- [04/11/2015 - P037] Instability of dewetting fronts in thin solid films, moted by Levy flights in an out-equilibrium system in Anna Chame, UFF-RJ -Brasil, Olivier Pierre- which the parity is conserved. This model is of great in- Louis, Universit´eLyon 1-CNRS, France Anisotropy terest to the scientific community working in phase tran- has an important effect in the dewetting dynamics of thin sitions and critical phenomena, since it is expected to solid films. Instabilities in the dewetting front morpho- present a universality class that differs from that com- logy have been experimentally observed [1, 2], for instance mon Directed Percolation - DP. We investigate the cri- in films of Si and Ge on SiO substrates. When an initial tical properties of this system using computational tech- 2 hole is produced in a thin film, its edges can be unstable, niques and finite-size scaling. Through the Monte Carlo and void fingers may develop. In the case of Si films, simulation method, we analyzed the region of transition these fingers grow along diagonal directions with respect on linear finite lattices with an odd number of sites and to the main axes of the film lattice, whereas in the case initially totally occupied. We estimate the critical point of Ge films, the fingers grow along axial directions. To p through the scale invariance of the particles density c investigate the effect of anisotropy in dewetting, we em- cumulant. After finding p , it was possible to determine c ploy kinetic Monte Carlo simulations to implement the the set of critical exponents that characterize the uni- dynamics, using a 2D solid-on-solid model. In this mo- versal behavior in the neighborhood of the second order del, epilayer atoms can hop to nearest neighbor sites and phase transition. From such analysis, we found a set of an atom needs to break all its bonds to hop, therefore exponents in agreement with the already presented in the the hopping barrier is given by the binding energy of the literature, besides new critical quantities which have not atom. The hopping rates also depend if the atom is in been studied previously for systems with parity conser- contact with the substrate or not. The model parameters vation and long range diffusion. Our results confirm that are the adsorbate-substrate excess energy E ,the tempe- the present model depicts a non-equilibrium phase tran- S rature T and the thickness h of the film. sition that don’t belong to the DP’s universality class. [1] F. Leroy, F. Cheynis, T. Passanante, P. Muller, Phys. Therefore, we can assert that a new set of critical expo- Rev. B 88, 035306 (2013). [2] C.V. Thomson, Annu. nents arises from the effects of parity conservation and Rev. Matter. Res. 42 399 (2012). long-range interactions. Further, we unveil that the criti- cal order parameter distribution evolves from the Gaus- [04/11/2015 - P038] sian to exponential form as the diffusion process becomes Dynamics of mean spherical model with correla- of longer range. ted noise, Masayuki Hase, Escola de Artes, Ciˆencias [04/11/2015 - P036] e Humanidades da Universidade de S˜ao Paulo, Malte Nonequilibrium statistical mechanics of electrons Henkel, Groupe de Physique Statistique, Institut Jean in a diode, Samuel Marini, Felipe B. Rizzato, Lamour (U. Lorraine) The dynamics of the mean sphe- Yan Levin, Renato Pakter, Instituto de F´ısica - rical model [1, 2, 3] with a dissipative term and a cor- UFRGS Fully kinetic descriptions of long-range self- related noise is investigated. This noise obeys a frac- interacting systems are generally very difficult to ob- tional brownian motion [4] with Hurst index H, and tain because these systems do not relax to the Maxwell- some mathematical techniques are proposed to obtain Boltzmann distribution and the tools of equilibrium sta- asymptotically exact results for large times. The analy- tistical mechanics cannot be employed. This is the case of sis is based on the two-time autocorrelation and response electron flows in diodes and in crossed-field devices which function, and the results are compared to the work of are fundamental for the development of several advan- Godr`eche-Luck [5], where the noise is uncorrelated (it is ced applications in areas ranging from microwave sour- worth noting that this problem has been considered be- ces to space propulsion, as well as in the semiconductor fore [6]). Comparing the two dynamics (which differ in industry. Here, a statistical theory is presented that al- the nature of the noise only), the present case shows a lows the calculation of the stationary state achieved by richer behavior, which is expected due to the presence of the electron in such systems after a process of collision- an extra parameter H; nevertheless, one can also observe ENFE - 04/11/2015 - Abstracts 69 the realization of some non-trivial interplay between dis- extincted depending on the initial state of the system. sipative part and noise term. By performing Monte Carlo simulations, we have analy- [1] T. H. Berlin and M. Kac, Phys. Rev. 86, 821 (1952) zed two different methods in order to maintain the system [2] H. W. Lewis and G. H. Wannier, Phys. Rev. 88, 682 out of the absorbing state. The first method introduces a (1952) small perturbation on the absorbing state replacing one [3] H. W. Lewis and G. H. Wannier, Phys. Rev. 90, 1131 particle of each species. In the second method, once the (1953) system reaches the absorbing state, this state is replaced [4] B. B. Mandelbrot and J. W. Van Ness, SIAM Review by a visited active one. Our results show that the bistable 10, 422 (1968) phase can be observed just with the first method. In this [5] C. Godr`eche and J. -M. Luck, J. Phys. A 33, 9141 case, a hysteresis loop appears either in the Erd¨os-R´enyi (2000) graph or in the complete one. Finally, this method can be [6] G. Ronca, J. Chem. Phys. 68, 3737 (1978) applied to low-dimensional systems, where it is possible to find a hysteresis loop which has its length depending [04/11/2015 - P039] Width and extremal height distribu- on the simulation time. tions of Kardar-Parisi-Zhang interfa- [04/11/2015 - P041] ces with window boundary conditions., Transfer-matrix study of a hard-square lattice Ismael Segundo da Silva Carrasco, Tiago Jose´ gas with two kinds of particles and density ano- de Oliveira, Universidade Federal de Vi¸cosa We maly, Tiago J. Oliveira, Departamento de F´ısica, present a detailed numerical study of squared local UFV, Jurgen¨ F. Stilck, Instituto de F´ısica, UFF and roughness (SLRDs) and local extremal height distri- INCT-SC Using transfer matrix and finite-size scaling butions (LEHDs), calculated in windows of lateral methods, we study the thermodynamic behavior of a lat- size l, for KPZ interfaces, in 1 + 1 and 2 + 1 di- tice gas with two kinds of particles on the square lattice. mensions. We show that their cumulants follow the Only excluded volume interactions are considered, so that Family-Vicsek type scaling, and, at early times (when the model is athermal. Large particles exclude the site the correlation length ξ is smaller than l), the nth they occupy and its four first neighbors, while small parti- SLRDs cumulant scale in time as w tγn , with cles exclude only their site. The correlations length of the h nic ∼ γn = 2nβ + (n 1)ds/z = [2n + (n 1)ds/α] β. This model defined on strips with finite widths and periodic scaling is featured− by small corrections,− providing expo- boundary conditions is found diagonalizing the transfer nents (α, β and z) in nice agreement with their respective matrix and the critical point is estimated using phenome- universality classes. Therefore, it is an useful framework nological renormalization. Two thermodynamic phases for numerical and experimental investigations, where it are found: a disordered phase where large particles oc- is, usually, hard to estimate the dynamic z and the (glo- cupy both sublattices with the same probability and an bal) roughness α exponents. At the stationary regime ordered phase where one of the two sublattices is prefe- (ξ l), we observe that SLRDs and LEHDs for small l’s rentially occupied by them. The transition between these can≫ present strong finite-size corrections, and the best phases is continuous at small concentrations of the small way to prove their universality is through extrapolations particles and discontinuous at larger concentrations, both (for long times and l’s) of their cumulant ratios. This transitions are separated by a tricritical point. Estimates shows that the procedure adopted in recent comparisons of the central charge suggest that the critical line is in of experimental and numerical/theoretical distributions, the Ising universality class, while the tricritical point has based on small l data collapse, could lead to misleading tricritical Ising (Blume-Emery-Griffiths) exponents. The conclusions. As final result, we demonstrate that SLRDs isobaric curves of the total density as functions of the fu- and LEHDs are the same for flat interfaces and curved gacity of small or large particles display a minimum in ones. We acknowledge FAPEMIG, CAPES and CNPq the disordered phase. It should be mentioned that since by the financial support. two particles are present in the model with distinct sizes, one may say that two length scales are involved in the interaction potential, a feature which has been proposed OTHER TOPICS to lead to density anomalies in models for water. [04/11/2015 - P040] [04/11/2015 - P042] High dimension analysis of the symbiotic two- Three wave nonlinear interaction: a multimode species contact process model, T. B. dos Santos, extension, P. Iorra, S. Marini, E. Peter, A. T. C. I. N. Sampaio Filho, A. A. Moreira, J. S. An- Chavez,´ F. B. Rizzato, Instituto de F´ısica, Universi- drade Jr., Grupo de Sistemas Complexos, Departa- dade Federal do Rio Grande do Sul The slow modula- mento de F´ısica, Universidade Federal do Cear´a In the tional approximation to the dynamics of high-frequency symbiotic contact process model each node in a graph can carrier waves has been proved time and time again as a be vacant, occupied by one or two particles of different powerful technique to deal with system with virtually in- species. The symbiotic interaction is represented by the finite degrees-of-freedom. Instead of describing the oscil- reduced death rate µ (0 <µ< 1) for a pair of parti- latory modes at their short space and time scales, the mo- cles in the same node. From the analytical analysis of dulational approach allows to obtain approximate gover- the mean-field theory, we show that the model undergoes ning equations for a smaller and much smoother varying a discontinuous phase transition at the critical creation set of dynamical variables: the amplitudes and phases of rate λc(µ), which is a decreasing function of µ.Moreover, the involved waves. we determine a region of bistability, where the system has Modulational techniques have been applied to a variety two stable states, namely, both populations persist or are of physical settings, ranging from mechanical waves in 70 Abstracts - ENFE - 04/11/2015 solids, to electromagnetic waves in plasma accelerators. behavior of the CPT’s as a function of the concentration In all cases, the needed condition for accuracy is that of solutes. The observed behavior of the adjusted pa- the wave interaction is weak enough that amplitudes and rameters can be interpreted in terms of the Hofmeister phases indeed change in a much larger space-time scale (or lyotropic) series. The reduced number of adjusta- than the high-frequency times scale and wavelength spa- ble parameters needed to reproduce some experimental tial scale of the carriers. data is one of the advantages of the proposed model over The modulational theory has been successfully applied to other theoretical approaches as activity-coefficient chemi- the study of three waves systems, where energy exchange cal models like UNIFAC or UNIQUAC. involving three wave modes is possible if parametric ins- [04/11/2015 - P044] tabilities is present. The wave triplet is a cornerstone in Thermal properties of a solid through of Fibonacci the study of nonlinear wave interaction and more com- oscillators, Andre´ Afonso Araujo Marinho, plex interactive system can be frequently understood with Francisco de Assis de Brito, UFCG We treat basis on three wave partitions. the study of the thermodynamics of a crystalline solid, Considering the importance of the three wave interaction, applying algebra of Fibonacci oscillators. As is known a recent work investigated the behaviour of the triplet a solid is formed by a large number of atoms connected dynamics as the coupling grows beyond the proper vali- by cohesive forces of various types. Each atom moves dity range for modulational approximations. It has been only in a small neighborhood, vibrating around its found that there exists indeed a critical coupling strength point of balance. The impurity states are located, and separating modulational and chaotic regimes, where in correspond the movement of electrons inside a space the latter amplitudes execute much larger and much fas- (structure) limited, resulting in some areas or types of ter oscillations than in the former. electronic interaction, i.e., the network is experiencing In the present work we shall focus on a multimode exten- a kind of electron rearrangement change in motion of sion of the triplet interaction to address the behaviour of nuclear spins, etc. In our study, we consider models this multimode system as the nonlinear coupling between Einstein and Debye. We applied to (q1, q2)-algebra and the various modes increase. The question to be examined deform the energy spectrum, we obtain a Hamiltonian here is basically whether or not a critical coupling factor (q1, q2)-deformed and hence thermodynamic quantities. is present defining a transition from a smoother to a less The interpretation of the results allowed the strain regular type of dynamics, similarly to what happens with acting as parameters factors disorder or impurities which an isolated triplet. alter the characteristics of a crystal structure, e.g., in As we shall see, a transition will be indeed identified and the case of semiconductors. The main results indicate argued to be of relevance to nonlinear wave fields with that we have more flexibility in adopting values for q1 cubic nonlinearities in the corresponding Lagrangian or and q2, we can imagine the future, a new element with Hamiltonian functions. ideal characteristics, or even occasionally improve an [04/11/2015 - P043] existing element. We need more studies and evidence to Aqueous two-phase systems of polyethylene gly- substantiate such a complex case. For example, we are col and inorganic salts: a statistical model, trying to establish a connection between this theory and Filipe Leoncio Braga, Instituto Federal de Educa¸c˜ao experiences through the growth of thin films, an issue e Tecnologia do Esp´ırito Santo, Rod. Gov. Jos´eSete, that will be addressed elsewhere. s/n - Itaciba, Cariacica - ES, 29150-410, Mario No- [04/11/2015 - P045] boru Tamashiro, Universidade Estadual de Campinas, Nonlinear Relaxation Time Model, Instituto de F´ısica ”Gleb Wataghin”, Departamento de D. S. Oliveira, R. M. O. Galvao,˜ Instituto de F´ısica Aplicada, Rua S´ergio Buarque de Holanda, 777 F´ısica, Universidade de S˜ao Paulo In the collisional - Bar˜ao Geraldo, Campinas-SP, 13083-859 Thermal- kinetic plasmas theory, the traditional approach lies on statistical models that try to reproduce the behavior of the use of an approximative collisional term in order aqueous polymer solutions have been extensively studied to avoid the issue of the full complicated equation. In over the years. However, the number of articles related to this work, we present a new simple nonlinear relaxation aqueous systems containing polymers and added salts is model based on two different relaxation times, namely, still very restricted. We investigate a model based on the τ1 and τ2. In contrast with many models in kinetic Flory-Huggins theory to analyze the formation of aque- plasmas theory, our model has the striking feature of not ous two-phase systems comprising long-polymer chains being directly linearized when the local thermodynamic of polyethylene glycol in mixtures containing monova- equilibrium is assumed. It is also proved that the lent inorganic salts. In the proposed statistical model model satisfies the H-theorem and the conservations the competition between the hydrogen-bond formation laws (particles, momentum and energy conservation among water molecules and the monomers of the polymer during the collisions). The basic theoretical framework chain, in addition to the ion-dipole interactions between is outlined and it is applied for three distinctive relevant water and the dissociated salt ions play a key role in sha- applications: 1) The relaxation to equilbrium in the ping the equilibrium configurations. Through numerical spatially homogeneous case. The expression found for fits of experimental data presented in the literature, for the distribuition function f shows that the nonlinear each type of salt introduced into the mixture, with model term can either accelerate or decelerate the relaxation predictions for the phase-separation temperatures, the so- process; 2) Electrons runaways in a cooling plasma. We called Cloud-Point Temperatures (CPT), we find a set of use the condition of vanish collision term, C(f) = 0, to four phenomenological interaction parameters that ena- find the distribution function f of the electrons in the bles proper theoretical representation of the continuous runaway phenomena; 3) Negative differential resistance ENFE - 04/11/2015 - Abstracts 71 in GaAs. In this application, the drift velocity and the the worm algorithms [2]. Devising these algorithms in- density of the electrons are calculated. In addition, the volves changing the original variables of the problem, the threshold electric field and the density of the electrons at “Potts spins”, to new ones that are known as flux vari- the upper conduction band are calculated and the values ables. One says that the introduction of these variables found show good agreement with other results present in corresponds to utilizing a flux representation (FR) for the literature. the VPM [3,4]. First we discuss how the description of [04/11/2015 - P046] the model can be reformulated in terms of the flux varia- Domain-size heterogeneity in the Ising mo- bles. Then we explain how the FR allows us to conceive del: Geometrical and thermal transitions, new Monte Carlo methods for studying the VPM. More- Andre´ R. de la Rocha, Jeferson J. Arenzon, Ins- over, we consider a second application of the FR to the tituto de F´ısica, Universidade Federal do Rio Grande do analysis of the VPM within the mean field approxima- Sul, CP 15051, 91501-970 Porto Alegre, Rio Grande do tion. Preliminary results – valid in this approximation – Sul, Brazil, Paulo Murilo C. de Oliveira, IMEA, for observables such as the magnetization are presented. Universidade Federal da Integra¸c˜ao Latino Americana, [1] F. Y. Wu, Rev. Mod. Phys. 54, 235 (1982). Foz do Igua¸cu, Paran´a, Brazil - Instituto de F´ısica, Uni- [2] N. Prokof’ev and B. Svistunov, Phys. Rev. Lett. 87, versidade Federal Fluminense, Niter´oi, Rio de Janiero, 160601 (2001). Brazil Cluster or domain size distributions are com- [3] Y. D. Mercado, H. G. Evertz and C. Gattringer, Phys. monly used in statistical mechanics to unveil geometric Rev. Lett. 106, 222001 (2011). properties and characterize both the equilibrium critical [4] Y. Mercado, H. Evertz and C. Gattringer, Computer behavior and the out of equilibrium dynamics of seve- Physics Communications 183, 1920 (2012). ral models. If the system is finite, not all possible do- [04/11/2015 - P048] main sizes are present on a single configuration. These Discrete Fields in Condensed Matter, sample-to-sample fluctuations disappear and the distri- Breno Rodrigues Segatto, Manoelito Mar- butions become dense in the infinite size limit, or after en- tins de Souza, UFES Fundamental interactions, semble averages are taken. In order to characterize these according to quantum field theory, are realized th- fluctuations, a quantity associated with how heterogene- rough the exchange of interaction quanta-packets of ously sized the equilibrium domains are, H, was recently matter-energy with defined quantum numbers, namely proposed in the context of explosive percolation and then momentum-energy, spin, electric charge, etc. They applied to ordinary random percolation and to domains are discrete interactions, in contradistinction to the of parallel spins in the Ising and Potts models. Differen- classical continuous picture. By a classical model of tly from the cluster size distribution, the heterogeneity H discrete interaction, we mean the replacement of the only takes into account whether a given size is present in potential representative of the continuous interaction, each configuration and gives the number of such distinct by the exchange of, in an evident abuse of language, sizes. In addition to geometric domains of parallel spins, classical quanta, little bits of well-defined amounts of for thermal spin models one can consider physical clus- energy-momentum. This classical quantum is emit- ters, which take into account the temperature-dependent ted/absorbed in an instantaneous process caused also correlation between neighboring spins and encode the cri- by the absorption/emission of a previous quantum. We tical properties of phase transitions. In this work we ex- intend to start a discussion about the formalism of tend the measure of H to these clusters and, moreover, discrete interactions in a non-relativistic regime, which present new results for the geometric domains in the Ising is appropriate for dealing within condensed matter, and model with d = 2 and 3. We show through extensive propose a model of two spin interacting, via Heisenberg Monte Carlo simulations that the heterogeneity associa- Hamiltonian, where the exchange interaction is via a ted with physical domains for d = 2 has a single peak discreet field that will be discuss during the presentation that diverges at the critical temperature, while for the where we will use the statistical physics to analyses the geometric domains it has a previously unnoticed double new terms that appear during the formalism. peak, presenting signatures for both the percolative and thermal transitions [1]. QUANTUM FLUIDS & CONDEN- [1] Phys. Rev. E 91, 042113 (2015) SED MATTER/ DISORDERED AND [04/11/2015 - P047] GLASSY SYSTEMS Flux representation for the vector Potts model, Marcio Woitek, Gastao˜ Krein, IFT-UNESP One [04/11/2015 - P049] of the models that have been most widely studied for A Lattice-Boltzmann Method for electrons in me- gaining insight on the ferromagnetic phase transitions is tals, Rodrigo C. V. Coelho, Mauro M. Doria, the so-called vector Potts model (VPM) with N states, a Universidade Federal do Rio de Janeiro, Anderson straightforward generalization of the Ising model [1]. It is Ilha, Instituto Nacional de Metrologia, Normaliza¸c˜ao e well known the fact that, except for some very particular Qualidade Industrial In the 80’s a numerical method values of N and of the dimension d of the correspon- was developed to solve the Boltzmann equation with the ding lattice, this model can not be studied in an entirely BGK (Bhatnagar, Gross and Krook) collision term. This analytical manner. Therefore, one can say that our un- method, based on the discretization of the phase space, derstanding about the VPM in the general case is based was very successful in solving various problems of fuid me- on results of computer simulations that employ Monte chanics, including problems with complex geometry, in- Carlo methods. A class of such methods that received terfacial phenomena and multicomponent fluids. Known considerable attention during the last decade is that of as the LBM - Lattice Boltzmann Method - it describes the 72 Abstracts - ENFE - 04/11/2015 evolution of a set of statistical distributions of particles theory, opening new possibilities for many models and defined on a regular space lattice in which each site has a possible magnetic phases. finite number of velocities directed to neighbouring sites. [04/11/2015 - P051] The advantage over other methods lies in the simplicity Electronic dynamics under effect of a of its dynamics and especially the flexibility for imple- nonlinear Morse interaction and a static mentation in parallel computing. In recent years, there electric field, Adhemar Ranciaro Neto, has been a great interest in the construction of an LBM Francisco Anacleto Barros Fidelis de Moura, able to describe fluids that are not described by Maxwell- Instituto de F´ısica - UFAL The problem concerning Boltzmann distribution, like semi-classical fluids (descri- the time-dependent behavior of an initially localized bed by Fermi-Dirac and Bose-Einstein distribution) and electronic wave-packet under effect of nonlinearity and a relativistic fluids (described by Maxwell-Juttner distribu- static electric field has attracted the interest of scientific tion). community. It is well known that, at the absence of In this presentation we derive a general mathematical fra- nonlinearity, a static electric field applied parallel to a mework that leads to new LBM models associated to ge- periodic lattice promotes the dynamic localization of neric equilibrium distribution functions. This framework a given initial wave-packet. Furthermore, the presence is based on our discovery of a new polynomial basis in Eu- of static electric field gives rise to an oscillatory beha- clidean space which yields the Hermite polynomial basis vior of the electron wave packet (also called ”Bloch in the special limit that the weight function becomes the oscillations”). The size of the region over which the Gaussian function. The equilibrium function is expan- electron oscillates and the period of these oscillations ded in this new basis and we discuss the order that must are inversely proportional to the magnitude of the static be considered to obtain the correct conservation laws. electric field. In this work we will make a contribution We also obtain the discrete lattices associated to the new by going forward on the understanding of electronic polynomial basis. As an application, we construct a LBM transport in low-dimensional nonlinear systems under capable of describing electrons in the Fermi surface and effect of uniform electric field. We study numerically show some numerical simulations. This particular LBM the one-electron dynamics in a one-dimension alloy in is a very promising one since it could be used to des- which that the atoms are coupled by a Morse potential. cribe the conduction of electrons in arbitrary geometries, In addition, we consider a static electric field parallel something of interest in condensed matter and also in to chain. Within our model, the electron transport is industrial applications. treated quantum-mechanically over the alloy in tight- [04/11/2015 - P050] binding approximation and the longitudinal vibrations PERCOLATION THEORY IN THE POTTS of the lattice are described by using classical formalism. MODEL, Tiago de Souza Farias, Jonas Mazi- The electron-phonon interaction was introduced by ero, UNIVERSIDADE FEDERAL DE SANTA MARIA considering the electron hopping as a function of the The Potts model may be used to describe several sys- effective distance between neighboring atoms. By solving tems, as e.g. the magnetic behaviour of some materials. numerically dynamic equations for electron and lattice In this model, the magnetic moment of each atom, known we can compute the spreading of an initially localized as spin, can assume a range of possible values and orienta- electronic wave-packet. We report numerical evidences tions which depend on the material under consideration. of the existence of an electron-soliton pair even at the The Hamiltonian of this model is given by: presence of electric field. We offer a detailed analysis of the dependence of this electron-soliton pair with the H = J cosθij magnitude of the electric field and the electron-phonon − i,j P interaction. where θij is the angle between two nearest neighbours [04/11/2015 - P052] spins and J is the energy exchange. This model may exhi- Dynamical class of a two-dimensional plasmonic bit a magnetic phase transition from ferromagnetism to Dirac system, Erica´ de Mello Silva, Universidade paramagnetism at a critical temperature Tc. This tempe- Federal de Mato Grosso Since the advent of graphene rature can be estimated via computational methods like, as a tunable plasmonic material, the dynamics of sur- for example, the Monte Carlo method. face plasmons became a hot research topic in nanophoto- Fractal lattices are scale-free structures, very commonly nics. Graphene plasmons have a high capability of light present in nature, that have interesting topological fe- confinement and have been considered feasible to me- atures, such as lacunarity and fractal dimension. These diate interactions between externally controlled signals geometrical properties can give a better perspective of the and small quantum systems, e.g. quantum dots. Howe- topological behavior of magnetism in general lattices. ver, in spite of significant progress in the field, graphene In this work, we have shown that the ferromagnetic phase plasmons damping is still a hinder for the realization of transition is related to the geometrical phase transition graphene-based plasmonic devices. In this sense we be- by the percolation theory. This theory studies the con- lieve it might be of interest to enlarge the knowledge on nection among clusters within the lattice and, through the dynamical class of two-dimensional plasmonic Dirac techniques such as image analysis, provides a mean for systems. According to the recurrence relations method, obtaining the Tc faster than some other methods. Ad- the dimensionality d and the shape σ of the realized Hil- ditionally, we compared the phase transition order for bert space are the static properties that characterize time different number of orientations and its relation to the correlation functions of a dynamical variable in a system geometry of general structures. These results presents a towards relaxation process. Therefore one can state if deep connection between geometry and phase transition different systems are dynamically equivalent if they have ENFE - 04/11/2015 - Abstracts 73 the same d and σ, i.e., identical relaxation functions, and [04/11/2015 - P054] such commonality may lead to deep connections between On the special properties of generalized harmo- nic systems within the n 0 replica approach, seemingly unrelated physical systems. We employ the → recurrence relations approach to obtain relaxation and Everton M. C. Abreu, Edson S. de Pinho, Univer- memory functions of density fluctuations and show that sidade Federal Rural do Rio de Janeiro Spin glass mo- a two-dimensional plasmonic Dirac system at long wave- dels are relevant until today because they provide the length and zero temperature belongs to the same dyna- simplest models to investigate underlying concepts like mical class of standard two-dimensional electron gas and disorder and frustration. They are endowed with a kind classical harmonic oscillator chain with an impurity mass. of phase transition and hence a kind of organization at low temperature. In order to study systems with quen- ched disorder, a proper treatment involves averaging the [04/11/2015 - P053] free energy, but this task, as well known, is very dif- Influence of disordered porous media in the ficult since we have to deal with the logarithm of the anomalous properties of a simple water model, partition function to calculate the free energy which is Alexandre Penteado Furlan, Instituto de F´ısica, “self-averaging”in the thermodynamic limit. However, Univeridade Federal do Rio Grande do Sul,, Carlos the average cannot be carried out directly because the Eduardo Fiore, Instituto de F´ısica, Univeridade de random variables occur inside the logarithm. Spin glasses S˜ao Paulo,, Marcia Cristina Barbosa, Instituto de are highly random systems, and in many of the standard F´ısica, Univeridade Federal do Rio Grande do Sul, The models, the nonrandom part is zero. This technique is phase behavior of systems of particles interacting via the therefore not generally applicable, though even for spin so-called core-softened (CS) potentials has received a lot glasses it is valid at high temperatures and can be used of attention recently. They show a repulsive core with a to generate high-temperature series expansions. At low softening region when particles are very close These CS temperatures and certainly below a spin glass transition can be modeled as continuous potentials or lattice gas temperature, one needs a non-perturbative way of ave- models. For the lattice structure the two competing sca- raging over disorder. And this is the idea behind the les arise from two equilibrium configurations: low density replica approach. In this work we will use the replica ap- and high density. This procedure generates models that proach to analyze the spectral properties of generalized are analytically and computationally tractable and that harmonic systems. A replica symmetry breaking analysis one hopes are capable of retaining the qualitative featu- is accomplished too. res of the real complex systems. The physical motivation behind these studies is the assumption that two length [04/11/2015 - P055] scales systems exhibit the same anomalous behaviors pre- Ghatak-Sherrington model with a random field in sent in water. Confirming this hypothesis a number of a random network, Amanda de Azevedo Lopes, continuous and lattice gas models show the presence of Rubem Erichsen Jr, UFRGS The statistical mecha- density, diffusion and structural anomalous behavior as nics of a three-state Ising spin-glass model with a Ghatak- observed in water. Within the other seventy-two ano- Sherrington crystal-field term and a random field term is malies, water has at very low temperatures two coexis- studied in the present work. A finite connectivity tech- ting amorphous phases with distinct densities: the low nique is used, in which each spin is connected to a fi- density amorphous (LDA) and high density amorphous nite number of other spins. The spins were connected phases (HDA). These two amorphous phases led to the according a Poisson distribution, the random field term hypothesis of the existence at higher temperatures of two followed a bimodal distribution and the bonds between liquid phases: a low density liquid and high density liquid the spins were considered uniform. Thus, there is only phases. Such conjecture establishes that the coexistence a connection disorder. We focused on determining how between these two liquid phases ends in a second critical the nature of the transition changes with the connectivity point or also called, liquid-liquid critical point (LLCP) and if there is a reentrant behavior of the phase bounda- [24]. Experiments for testing the existence of this criti- ries. The replica technique is used to obtain saddle-point cality are difficult since the region in the pressure ver- equations for the effective local-field distribution. The sus temperature phase diagram where the alleged critical replica symmetric ansatz for the order function is writ- point exists is locate beyond the homogeneous nucleation ten in terms of a two-dimensional effective-field distribu- limit. In order to circumvent this difficulty for testing tion, where one of the components is associated with a the existence of the liquid-liquid critical point recently linear form in the spins and the other with the crystal- confined geometries have been employed. In this sense field term. This allows us to derive equations for the order the thermodynamic, dynamic and structural behavior of function and for the free-energy. A population dynamics a water-like system confined in a matrix is analyzed for procedure is used to solve numerically a self-consistency increasing confining geometries. The liquid is modeled equation for the distribution of the local field and with by a two dimensional associating lattice gas model that it some physical parameters, like magnetization and free- exhibits density and diffusion anomalies, in similarity to energy. Our results indicate that for the bimodal distri- the anomalies present in liquid water. The matrix is a bution there is a tricritical point, whose location is stron- triangular lattice in which fixed obstacles impose restric- gly dependent on c. The tricritical point is suppressed tions to the occupation of the particles. We show that below a certain minimum value of connectivity. obstacules shortens all lines, including the phase coexis- tence, the critical and the anomalous lines. The inclusion of a very dense matrix not only suppress the anomalies but also the liquid-liquid critical point. 74 Abstracts - ENFE - 04/11/2015 [04/11/2015 - P056] Oral sessions (11:00-12:30) PACKING OF DISKS ON A TWO DIMENSI- ONAL CAVITY WITH DILUTED PINS, Wel- lington Castro Ferreira, Valdemiro da Paz NONLINEARITY AND CHAOS Brito, Jose´ Pimentel de Lima, UFPI, Marcelo Andrade de Filgueiras Gomes, UFPE The phy- [04/11/2015 - 11:00 - Room Tubar˜ao] sics of two-dimensional systems have fascinating beha- Dynamics and indirect finite-time synchroniza- vior, and can also be surprisingly different from physics in tion of chaotic systems, Hilda A. Cerdeira, Insti- three dimensions. This has stimulated the study of sta- tuto de F´ısica Te´orica - UNESP, Universidade Estadual tistical properties of several systems such as monolayer Paulista, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II, packing configurations of a string of beads [1], as well as, Barra Funda, 01140-070 Sao Paulo, Brazil We addres- two-dimensional systems involving hard discs on a flat ses the problem of finite-time synchronization of tunnel cell. These systems have been subject of continued inte- diode based chaotic oscillators. After a brief investigation rest in physics, because they have connections with many of its chaotic dynamics, we propose an active adaptive fe- problems, as e.g. in the study of elastic and inelastic de- edback coupling which accomplishes the synchronization formation of polymers, and the study of fundamental pro- of tunnel-diode-based chaotic systems with and without perties of condensed matter, including structural phase the presence of delay(s), basing ourselves on Lyapunov transitions, among others. In this contribution it is inves- and on Krasovskii-Lyapunov stability theories. This fe- tigated the problem of the packing of hard discs on a two edback coupling could be applied to many other chaotic dimensional cell with fixed cylindrical pins which are obs- systems. A finite horizon can be arbitrarily established tacles with a much smaller diameter than the disks. The by ensuring that chaos synchronization is achieved at a cell consists of two rectangular sheets of acrylic separated pre-established time. An advantage of the proposed feed- by a thickness that allows to accommodate only a single back coupling is that it is simple and easy to implement. layer of discs. More than two hundred configurations of The case of relay-coupled oscillators in a small network such packing were analyzed and grouped by considering of three chaotic oscillators will be discussed in detail the density of pins and the nature of their distribution [04/11/2015 - 11:20 - Room Tubar˜ao] (square lattice or random lattice), all them obtained in Chaos in MEMs/NEMs resonators, the limit of maximum packing density. Working with the Wellington G. Dantas, Andre´ Gusso, Uni- digitized image of each configuration, the centroid of each versidade Federal Fluminense The Galerkin’s method disk was determined. The packing of disks was analyzed is used to derive a consistent one degree of freedom as a function of the number of obstacles and it was repre- (1DOF) model for a suspended fixed-fixed beam mi- sented as configurations of Wigner-Seitz (WS) cells. We cro/nanoelectromechanical (MEM/NEM) resonator found that the cellular structure of packaged discs follows including the contributions of geometric non-linearity a statistical description already described by Weaire and and the Casimir force. This model goes beyond the Rivier [2], in the partial characterization of random struc- parallel plate approximation by including the main tures in two dimensions in several aspects as, the distri- correction to the electrostaic and Casimir forces due butions of angles and the number of sides of the WS cells. to the beam curvature. The chaotic regime found in a The distribution of sides for the WS cells was analyzed small region of the parameter space close to the dynamic and compared with the Shackelford-Masaryk hypothesis, pull-in is fully characterized by means of the calculation and we also found that the arguments of Buechner et al. of the Lyapunov exponent and bifurcation diagrams. [3] do not apply to this study to explain the lognormal The comparison with results presented in the literature, distribution proposed in [3]. Additionally we verified a obtained using much more computationally demanding reasonable agreement with the Aboav’s law [4]. The pair approaches, evidences the reliability of the proposed correlation function was calculated for the centroid of the 1DOF model, and the relevance of incorporating the discs and the results suggest the characterization of the effects of beam curvature in simplified models of beam properties of the system in periodic, hexatic and random dynamics when large displacements are involved. We go regimes, which depend of the density of pins. further on that analysis studying similar systems and [1] Brito,V.P., Castro,W.S., Coelho,A.S.O., Go- trying to stablish the sources to the appearing of this mes,M.A.F., Physica A, 342(2004)419. [2] Weaire,D.; chaotic regime in such devices. A systematic analysis Rivier,N. Soap, Contemporary Physics, 25(1984)59. [3] has been carried out in order to understand all possible Buechner,C., Schlexer,P, Lichtenstein,L, Stuckenholz,S, regimes to the vibration of those resonators using as Heyde, and Freund,H-J, Z. Phys. Chem, 228(2014)587. control parameters three typical quantities in those [4] Hilhorst,H.J. Journal Physics A, 39(2006)7227. devices. Some modifications in its architecture or in the dissipation mechanism modelling are made, trying to stablish the robustness of each dynamical regime. [04/11/2015 - 11:35 - Room Tubar˜ao] Finite-time generalized high-order Lyapu- nov exponents for kicked double rotor, Rodrigo Frehse Pereira, Federal University of Technology - Paran´a The ordinary Lyapunov ex- ponents spectrum describes the average exponential expansion/shrinkage rates of the axis of an infinitesimal ball around a trajectory under the temporal evolution ENFE - 04/11/2015 - Abstracts 75 of a dynamical system. These exponents are given ping. The dynamics can be basically described as a free by the linearization of the ruling equations. Due to particle that collides with a vibrating plate under the intrinsic nonlinearities present in models that present influence of a constant gravitational field. The dissipa- chaotic dynamics, nonlinear effects, swept off by the tion is introduced via a restitution coefficient between the linearization, can be crucial in elucidating details of the vibration platform and the free particle. The perturba- temporal evolution of such systems. Moreover, since tion parameter is set as a ratio between accelerations of Lyapunov exponents are dynamic invariants computed the particle and the moving platform. For low dissipa- as an average over an ergodic trajectory, they are tion regime, the root mean square velocity of the parti- ”blind”about local/finite-time fluctuations present in cle grows for short times, pass through a crossover and typical chaotic dynamical systems. We present a detailed then bend towards a stationary state. This behaviour analysis of the finite-time fluctuations of the generalized is characterized by scaling laws. When high dissipation high-order Lyapunov exponents for a physical system is considered, the dynamics evolves to different attrac- composed of a periodically kicked double rotor. We tors. The evolution of the basins of the attracting fixed focus in its chaotic regime and in the transition from points is characterized, as we vary the control parame- chaos to hyper-chaos as the intensity of the kicks is ters. Crises between the attractors and their boundaries increased. Generalized high-order Lyapunov exponents are observed. We found that the multiple attractors are are given by the analysis of high-order derivatives of the intertwined, and when the boundary crisis between their dynamical equations, which define linear mappings and stable and unstable manifolds occur, it creates a succes- their effects over the Lyapunov vectors are studied in a sive mechanism of destruction for all attractors originated similar manner done for ordinary Lyapunov exponents. by the sinks. Also, a physical impact crises is described, We study the temporal fluctuations of these high-order an important mechanism in the reduction of the number Lyapunov exponents for finite-time trajectories and of attractors. relate their properties with those observed in the chaos / hiper-chaos transition. q-STATISTICS [04/11/2015 - 11:50 - Room Tubar˜ao] Defining universality classes for three different lo- [04/11/2015 - 11:00 - Room Vit´oria] cal bifurcations, Edson Denis Leonel, UNESP - Thermodynamic Framework for a Nonextensive System, Fernando D. Nobre, Evaldo M.F. Cu- Departamento de F´ısica The convergence to the fixed point at a bifurcation and near it is characterized via rado, Centro Brasileiro de Pesquisas F´ısicas, Andre scaling formalism for three different types of local bifur- M.C. Souza, Departamento de F´ısica, Universidade Fe- cations of fixed points in differential equations, namely: deral de Sergipe, Roberto F.S. Andrade, Instituto de (i) saddle-node; (ii) transcritical; and (iii) supercritical F´ısica, Universidade Federal da Bahia Recently, an ef- pitchfork. At the bifurcation, the convergence is descri- fective temperature θ was introduced within the context bed by a homogeneous function with three critical expo- of interacting vortices in type II superconductors. The nents α, β and z. A scaling law is derived hence relating quantity θ was shown to represent an appropriate defini- the three exponents. Near the bifurcation the evolution tion of effective temperature for this system, exhibiting towards the fixed point is given by an exponential func- properties very similar to those of the usual thermody- tion whose relaxation time is marked by a power law of namic temperature T , being: (a) A positive quantity by the distance of the bifurcation point with an exponent δ. definition; (b) Thermodynamically conjugated to a gene- The four exponents α, β, z and δ can be used to defined ralized entropy per particle, sq with q = 2, characteristic classes of universality for the local bifurcations of fixed of nonextensive statistical mechanics. In this way, a heat points in differential equations. The formalism is proved contribution was defined, δQ = θds2; (c) Proportional to to be valid and can be used in either mappings and non- the density of vortices n. This property yields the desi- linear differential equations. In a family of logistic-like rable possibility for varying θ, since recent experimental γ researches in type II superconductors led to considerable mapping of the type xn+1 = Rxn(1 xn), the exponent α is independent on the nonlinearity of− the mapping while advances in the ability of controlling many properties of both β and z do indeed depend on γ for both transcritical these vortices, including their density; (d) Characterized and saddle-node bifurcation. The critical exponents for by values that are much higher than typical room tempe- the period doubling bifurcation however do not depend ratures (θ T ), so that the thermal noise can be neglec- ted as a good≫ approximation (T/θ 0); (e) Physically in- on γ and seem to be universal. Because of the so called ≃ normal forms, the three main bifurcations above mentio- terpreted in terms of the variance of the vortex positions, 2 3/2 ned can be observed in a set of three distinct differential θ x ; (f) Consistent with the definition of a Carnot cycle,∝ h whosei efficiency was shown to be η =1 (θ /θ ), equations. The present approach can be an alternative − 2 1 to define classes of universality in local bifurcations both where θ1 and θ2 represent the effective temperatures asso- in mappings and in differential equations. ciated with the isothermal transformations of the cycle, with θ1 > θ2. In order to achieve this later result, an [04/11/2015 - 12:05 - Room Tubar˜ao] infinitesimal-work term δW was introduced, leading to a Crises in a non-conservative bouncer model, proposal for the first law of thermodynamics. In the pre- Andre´ L. P. Livorati, Carl P. Dettmann, Ibereˆ sent work we explore the heat contribution, δQ = θds2, L. Caldas, Edson D. Leonel, Departamento de F´ısica by considering systems in thermal contact in such a way - UNESP - campus de Rio Claro The dynamics of a to exchange heat among themselves. Important concepts bouncing ball model under the influence of dissipation is like thermal equilibrium and heat reservoir are introdu- investigated by using a two dimensional nonlinear map- ced, and particularly, the zeroth principle is established. 76 Abstracts - ENFE - 04/11/2015 Moreover, we consolidate the first-law proposal by fol- nomy. Using a wide array of statistical tools including lowing the usual procedure for obtaining different poten- entropy concepts and complex systems theory, the tials, i.e., applying Legendre transformations for distinct present work proposes to investigate time series that pairs of independent variables. From these potentials we exhibit variabilities in a very broad spectrum of research derive the equation of state, Maxwell relations, and de- interests, ranging from astrophysical noise, rotational fine response functions. All results presented are shown modulation and pulsation to planetary transit and to be consistent with those of standard thermodynamics explosive events. Thus, we intent have been to develop for T > 0. a powerful statistical environment for study of nonsta- tionary, nonlinear, quasi-periodic, unevenly spaced, and [04/11/2015 - 11:20 - Room Vit´oria] The standard map as an example of crossing non-equilibrium time series in astrophysics. For that, from Boltzmann-Gibbs statistics to Tsallis statis- our research will point toward the stochastic processes tics., Ugur Tirnakli, Ege University, Izmir, Turkey, associated to dynamical complexity in time series from Ernesto P. Borges, Universidade Federal da Bahia Kepler spacecraft telescope. No doubt, dynamical complexity is a phenomenon expected to be observed As well known, Boltzmann-Gibbs statistics is the cor- rect way of thermostatistically approaching ergodic sys- in astrophysical time series when normal and abnormal tems. On the other hand, nontrivial ergodicity break- states (e.g. pre-storm activity and magnetic storms) down and strong correlations typically drag the system are detected. In this context, distinct physical effects into out-of-equilibrium states where Boltzmann-Gibbs in the stellar photosphere associated to large and short statistics fails. For a wide class of such systems, it has variabilities and multifractal structure can be discrimi- been shown in recent years that the correct approach is to nated using diagnostic tools for forthcoming extreme use Tsallis statistics instead. Here we show how the dyna- events. In our case, these phenomena are characterized mics of the paradigmatic conservative (area-preserving) by an entropic index q which leads to a nonextensive standard map, exhibits, in an exceptionally clear man- statistics. In several scenarios, time-dependent q-entropy ner, the crossover between both statistics. Our results effectively detects with a high precision small and crucial unambiguously illustrate the domains of validity of both details in dynamics of the signal, where the vast majority Boltzmann-Gibbs and Tsallis statistics. The standard of statistical techniques fails. The results show that Tsallis entropy can effectively detect the dissimilarity of map is defined as pi+1 = pi K sin xi, xi+1 = xi + pi+1, where p and x are taken as− modulo 2π. This map has complexity between the different variabilities present in very rich properties depending on the map parameter K. our sample. The phase space of the standard map presents regions [04/11/2015 - 11:50 - Room Vit´oria] of positive Lyapunov exponents coexisting with regions Non-additivity and Complex Systems, of zero Lyapunov exponents. The positive Lyapunov re- Marcelo A. Moret, UNEB e SENAI-CIMATEC gions present mixing and thus the system is ergodic in Many complex physical, chemical, economical, and those regions. For sufficiently low values of the control biological systems manifest non-additivity characterized parameter K, the phase space is almost entirely domi- by long-tail distributions. Recently, we studied different nated by zero Lyapunov behavior and the distributions time series that presented non-additive behavior in (obtained through time averaging, along the lines of cen- astrophysical sources, neuronal responses, dengue fever tral limit theorems) are q-Gaussians. As the value of epidemics, proteins, sunspots, vehicle demand on the K increases the measure of the zero Lyapunov regions ferry-boat system, among others. That said, we studied decreases, and we see a continuous crossing between q- light curves coming from astrophysical systems. We Gaussians distributions (Tsallis statistics) and Gaussian observe that astrophysical objects obey q-Gaussian ones (Boltzmann-Gibbs statistics). Remarkably enough, distribution as probability density and the q-value the distributions originated from initial conditions taken increases for systems when the Tsallis entropy decreases. inside the region of islands, instead of over the entire The classical concepts establish that the magnitude of phase space, yield one and the same value q =1.935, in- spontaneous miniature end-plate potentials of mammals dependently on whether we consider one or many of these recorded at neuromuscular junctions is characterized by regions, and independently from K. Initial conditions ta- Gaussian statistics and that their intervals are randomly ken within the chaotic sea always yield Gaussians. Since displayed, but it is not true. Power laws of protein various important physical systems from particle confi- mass, volume and solvent-accessible surface area are nement in magnetic traps to autoionization of molecular observed and q-Gaussian distributions fit well for this Rydberg states, through particle dynamics in accelera- class of systems. When we analyzed the time series tors and comet dynamics, can be reduced to the standard of vehicle demand on the ferry-boat system we note map, our results are expected to enlighten and enable an that stationary states of this dynamics process can be improved interpretation of diverse experimental and ob- obtained by a nonlinear Fokker-Planck equation. On servational results. the other hand, the distribution of the sunspots obeys [04/11/2015 - 11:35 - Room Vit´oria] a q-exponential decay that suggests a non-extensive A NEW INSIGHT ABOUT THE STELLAR behavior. This observed characteristic seems to take VARIABILITY USING NONEXTENSIVE EN- an alternative interpretation of the sunspots dynamics. TROPY: FROM ASTROPHYSICAL NOISE The present findings suggest us to propose a dynamic TO EXOPLANETS, Daniel B. de Freitas, model of sunspots formation based on a nonlinear DFTE/UFRN Time series analysis is an enormous Fokker-Planck equation. The number of epidemiological field of study in mathematical statistics, econometrics, dengue cases for each city follows a Self-Organized signal processing, and other fields, among them, astro- Criticality behavior (SOC). However, the analysis of ENFE - 04/11/2015 - Abstracts 77 the number of cases in Bahia exhibits a q-exponential Superior (CAPES) are acknowledged for partial financial distribution. To understand this different behavior, we support. analyzed the distribution of the power law of SOC (γ) for all biomes of Bahia. Finally, we show in this paper that nature often behaves as non-additive object and, sometimes, non-extensively. [04/11/2015 - 12:05 - Room Vit´oria] Time reversibility for stochastic dynamics with multiplicative noise, Zochil Gonzalez´ Arenas, Departamento de Matem´atica Aplicada, IME, Univer- sidade do Estado do Rio de Janeiro, Daniel G. Barci, Miguel Vera Moreno, Departamento de F´ısica Te´orica, Universidade do Estado do Rio de Janeiro Stochastic differential equations and its applications is a subject of great interest for scientific research. In this area, Langevin and Fokker-Planck formalisms are exten- sively used. Systems modeled by differential stochastic equations with additive noise have been largely studied and are the most popular models. However, the unders- tanding of the stochastic dynamics and the evolution to equilibrium for systems dealing with multiplicative noise is difficult and there is a lack of general tools for its cha- racterization. In particular, for the multiplicative noise case, the Fokker-Planck equation does depend on the cho- sen prescription for the stochastic integration of the as- sociated Langevin equation. In such case, it is possible for time evolutions to reach non-Boltzmann equilibrium states. To deal with these systems, we use a general prescription α for considering the stochastic integration. α is defined as a continuous parameter, 0 α 1, and each of its values corresponds with a different≤ discretization≤ rule for the stochastic differential equation. α = 0 corresponds with Itˆoprescription at the time that α = 1/2 corres- ponds with Stratonovich one. We also represent the sto- chastic process in a functional Grassman formalism [1], which turns out to be very convenient for handling sto- chastic trajectories. In this work [2-4], we study equilibrium properties of Mar- kovian multiplicative white-noise processes. For this, we carefully define the time reversal transformation for this kind of processes, taking into account that the asymp- totic stationary probability distribution depends on the prescription. In white noise multiplicative processes, sto- chastic trajectories evolve with different prescriptions in one direction and in the reverse direction. We show that, using a careful definition of equilibrium distribution and taken into account the appropriate time reversal trans- formation, usual equilibrium properties, such as detailed balance, are satisfied for any prescription. [1] Zochil Gonz´alez Arenas and Daniel G. Barci, Phys. Rev. E81, 051113 (2010); Phys. Rev. E 85, 041122 (2012) [2] Zochil Gonz´alez Arenas and Daniel G. Barci, J. Stat. Mech. P12005.(2012) [3] Zochil Gonz´alez Arenas, PhD Thesis, CDU 53 : 519.2, UERJ, 2012. [4] Miguel V. Moreno, Zochil Gonz´alez Arenas and Daniel G. Barci, Phys. Rev. E91, 042103 (2015). The Brazilian agencies, Funda¸c˜ao de Amparo `aPesquisa do Estado do Rio de Janeiro (FAPERJ), Conselho Nacio- nal de Desenvolvimento Cient´ıfico e Tecnol´ogico (CNPq) and Coordena¸c˜ao de Aperfei¸coamento de Pessoal de N´ıvel 78 Abstracts - ENFE - 04/11/2015 Oral sessions (14:30-16:05) with the percolation backbone structure via the relation α =2 d , where d is the backbone fractal dimension. − B B [04/11/2015 - 15:05 - Room Tubar˜ao] COARSENING AND INTERFACES Experimental Realization of Interfacial Fluc- tuations in the Kardar-Parisi-Zhang Universa- [04/11/2015 - 14:30 - Room Tubar˜ao] lity Class: A Non-Orthodox Approach & Its Coarsening in inhomogeneous systems, Consequences for Kinetic-Roughening Status, Federico Corberi, Salerno University - Italy I will R. A. L. Almeida, S. O. Ferreira, Universidade Fe- review the topic of coarsening phenomena occurring deral de Vi¸cosa, Minas Gerais, Brazil, T. J. Oliveira, in ferromagnetic systems where quenched features - Iowa State University, Ames, United States, F. D. A. A. such as random field, varying coupling constants or Reis, Universidade Federal Fluminense, Rio de Janeiro, lattice vacancies - spoil homogeneity. I will discuss Brazil The Kardar-Parisi-Zhang (KPZ) Universality the current understanding of the problem in systems Class has been helding a central, cornerstone position in with a non-conserved scalar order parameter by focu- the realm of non-equilibrium Physics since the seminal sing primarily on the form of the growth-law of the work of KPZ in 1986 [1]. Inspired by Landau-Ginzburg ordered domains and on the scaling properties. A Theory from Equilibrium Statistics, KPZ proposed the general picture emerges characterized by two possible simplest, local, continuum and non-linear equation to growth-laws, either logarithmic or algebraic, connected describe the dynamic of growing surfaces. Unexpectedly, by a crossover phenomenon. In systems where lack of since then, the KPZ class has been showing to underlie homogeneity is due to dilution an interpretation of these the behaviour of a rich family of equilibrium and out- two growth-forms can be given in terms of the topology of-equilibrium phenomena beyond its initial purpose. of the underlying diluted network hosting the magnetic Examples touch models for protein traffic flow, global system. In particular, a conjecture is proposed where a paths of random walks in random landscapes, lines in logarithmic or a power-law growth are associated to the superconductors, coffe-rings’ effect, besides a striking, presence/absence of an equilibrium phase-transition. I wonderful connection to random matrices theory. While will discuss how such a conjecture is supported by the most advances have been done in d = 1 + 1 dimensions, results of numerical simulations of paradigmatic model tying theory, simulations and an increasing number of systems such as the Ising model with either site or bond experiments in a KPZ triumvirate, much less attention diluted, both in the case of a stochastic dilution and in has been paid to 2 + 1 due to the inexorable difficulties to that of deterministic fractal graphs. The relevance of handle mathematically, numerically and experimentally this to the case of different systems with other sources of such systems. As consequence, 2D-KPZ experiments, inhomogeneities will be also discussed. for instance, were not convincingly demonstrated until [04/11/2015 - 14:50 - Room Tubar˜ao] last year [2,3]. In this talk, we show an unprecedented Transition from compact to porous films in depo- experimental realization of 2D-KPZ by keeping track sition with temperature activated diffusion, D. di on fluctuations at interface of CdTe thin-films grown on Caprio, CNRS (France), Fabio´ D. A. Aarao˜ Reis, Si. Critical exponents are unearthed and demonstrated Universidade Federal Fluminense We study a thin film to agree with numerical results for 2D-KPZ models. growth model with temperature activated diffusion of ad- Going further the orthodox analysis, we experimentally sorbed particles, allowing for the formation of overhangs demonstrate that: i) An universal, rescaled Height and pores, but without detachment of adatoms or clusters Distribution (HD), upper dimensional counterpart of the from the deposit. Simulations in one-dimensional subs- Tracy-Widom distribution, emerge in the system. Inte- trates are performed for several values of the diffusion- restingly, a non-integer Gumbel distribution seems to fit to-deposition ratio R of adatoms with a single bond and well HD data. ii) Squared Local Roughness Distributions of the detachment probability ǫ per additional nearest exhibit striking agreement with numerical simulations neighbor (NN), respectively with activation energies are of lattice models, revealing a new universal signature Es and Eb. If R and ǫ independently vary, regimes of of KPZ, highlighted by its stretched exponential decay. low and high porosity are separated at 0.075 ǫc 0.09, iii) Connection with statistics of extremes provide other with vanishingly small porosity below that point≤ ≤ and fi- universal distribution for 2D-KPZ systems. In the last nite porosity for larger ǫ. Alternatively, for fixed values part, we show how to use i-iii) to uncover the possible of Es and Eb and varying temperature, the porosity has KPZ universality in fluctuating surfaces when poor a minimum at Tc, and a nontrivial regime in which it statistics and strong finite-time effects are unavoidable, a increases with temperature is observed above that point. common experimental situation. We use this scheme to This is related to the large mobility of adatoms, resem- analyse the temperature effect on our experimental KPZ bling features of equilibrium surface roughening. In this system. Finally, consequences of i-iii) into the current high-temperature region, the deposit has the structure of Kinetic-Roughening Status are addressed. a critical percolation cluster due to the non-desorption. The pores are regions enclosed by blobs of the correspon- The authors acknowledge support from FAPEMIG and ding percolating backbone, thus the distribution of pore CAPES. τ˜ size s is expected to scale as s− withτ ˜ 1.45, in reaso- nable agreement with numerical estimates.≈ Roughening [1] M. Kardar, G. Parisi, and Y.-C. Zhang, Phys. Rev. of the outer interface of the deposits suggests Villain- Lett. 56, 889 (1986). Lai-Das Sarma scaling below the transition. Above the [2] R. A. L. Almeida, S. O. Ferreira, T. J. Oliveira, and transition, the roughness exponent α 0.35 is consistent F. D. A. Aar˜ao Reis, Phys. Rev. B 89, 045309 (2014). ≈ ENFE - 04/11/2015 - Abstracts 79 [3] R. A. L. Almeida, et al., Europhys. Lett. 109, 46003 gion. The clusters spontaneously break chiral symmetry (2015). and rotate; they also display a nematic ordering with spi- ral patterns. We can also determine the growth law for [04/11/2015 - 15:20 - Room Tubar˜ao] the size of these clusters. Interface fluctuations for deposi- On the other hand, for the phase without aggregation, tion on enlarging flat substrates., we determine the translational and rotational diffusion Ismael Segundo da Silva Carrasco, Tiago Jose´ properties. Different regimes can be observed, depending de Oliveira, S´ılvio da Costa Ferreira Junior,´ on the combination of the random noise, the activity and Universidade Federal de Vi¸cosa, Kazumasa A. Ta- the density of the system. These results can be compa- keuchi, The University of Tokyo We investigate red with experimental results found in bacterial suspen- solid-on-solid models that belong to the Kardar-Parisi- sions. Unusual increase with density of the rotational Zhang (KPZ) universality class on substrates that diffusion is also found and explained as due to particle expand laterally at a constant rate by duplication of clustering. Large deviation functions for dumbell veloci- columns. Despite the null global curvature, we show that ties have been finally determined showing the appearance all investigated models have asymptotic height distribu- of non-singular behaviour. tions and spatial covariances in agreement with those expected for the KPZ subclass for curved surfaces. In 1 + 1 dimensions, the height distribution and covariance SOCIAL DYNAMICS are given by the GUE Tracy-Widom distribution and the Airy process instead of the GOE and Airy foreseen [04/11/2015 - 14:30 - Room Vit´oria] 2 1 Society Collapse through erroneous for flat interfaces. These results imply that when the Annual Tax rates: Piketty Recipe, KPZ class splits into curved and flat subclasses, as Paulo Murilo Castro de Oliveira, UFF/UNILA conventionally considered, the expanding substrate may A simple N-agents dynamic model is introduced with play a role equivalent to, or perhaps more important two ingredients: than, the global curvature. Moreover, the translational I) During the year, agents are randomly tossed to incre- invariance of the interfaces evolving on growing domains ase their wealth. Tossed agent i doubles its wealth W allowed us to accurately determine, in 2 + 1 dimensions, i towards 2W . The tossing is repeated N times, one agent the analog of the GUE Tracy-Widom distribution for i could be tossed more than once. Then, the wealth distri- height distribution and that of the Airy process for 2 bution is kept normalized W = 1. spatial covariance. Temporal covariance is also calcula- i i II) At the year end, all agents pay their annual taxes with ted and shown to be universal in each dimension and rates pW (net tax pW 2), whereP p is a control parameter. in each of the two subclasses. A logarithmic correction i i Then, the wealth distribution is again kept normalized, associated with the duplication of columns is observed W = 1. and theoretically elucidated. Finally, crossover between i i (As a matter of technicality, the normalization is per- regimes with fixed-size and enlarging substrates is also formedP because we are not interested in the economy investigated. We acknowledge FAPEMIG, CAPES and growing as a whole, only in the distribution of wealths CNPq by the financial support. and its inequalities. For those interested in it, we can [04/11/2015 - 15:35 - Room Tubar˜ao] inform that the factor 2 warrants an forever-growing eco- Diffusion, fluctuations and coarsening in an ac- nomy.) tive dumbbell system, Giuseppe Gonnella, Le- For p = 0, all agents pay the same tax rate. After many ticia Cugliandolo, Antonio Suma, Dipartimento di years, the whole society collapses, i.e. a single agent owns Fisica dell’Universit`adi Bari Active matter refers to the whole wealth. This situation is an absorbing state. systems driven out of equilibrium by energy sources conti- For p> 0, rich agents pay larger taxes than poor agents. For p larger than a critical value p 0.3 the collapse nuously transformed into movement or work on the envi- c ≈ roment. These systems exhibit many peculiar properties is avoided, the distribution of wealths survives forever not present in their passive counterparts, like clustering, and the absorbing state is never reached. So, there is anomalous diffusion and fluctuations, unexpected rheolo- a transition at pc. An order parameter for this transi- gical properties. tion is constructed by ordering the wealth distribution in Here, we will review the results obtained from the study decreasing order (Zipf plot), and calculating its first mo- of a two-dimensional system of active dumbbells, introdu- ment. The result is obviously null for p [1] Leandro B. Krott, Jos´eR. Bordin and Marcia C. Bar- bosa. New Structural Anomaly Induced by Nanoconfine- ment. J. Phys. Chem. B, v. 119, p. 291-300, 2015. 84 Abstracts - ENFE - 04/11/2015 Index Odor,´ G., 10 Bonin, C., 50 Bordin, J. R., 17, 82, 83 A Neto, M. A., 45 Borges, E. P., 76 Abreu, E. M. C., 8, 73 Borrero, P. P. G., 41 Aguiar, F. M., 16 Borsato, N. G., 38 Aguiar, M. A. M., 16, 52 Bortolotto, G. S., 30, 65 ALCARAZ, F. C., 67 Bosco, G., 6 Alcaraz, F. C., 55 Braga, F. L., 70 Almarza, N. G., 50 Braunstein, L. A., 54 Almedia, R. M., 24 Brigatti, E., 53 Almeida, D. F., 34 Brito, C., 18, 51, 53 Almeida, R. A. L., 78 Brito, F. A., 70 Almeida, R. M. C., 23 Brito, S. G. A., 2, 3 Alves, F., 3, 34 Brito, V. P., 11, 74 Alves, N. A., 39 Brito2, A. M. S., 31 Alves, S. G., 30, 43 Brum, R. M., 4 Alves, W. S., 19, 38 Brunnet, L. G., 23, 24, 58, 59 Amado†, A., 4 Bueno, L., 6 Amaral, M. A., 6 BV, C., 26 Amarante, T. D., 60 Amato, M. A., 9, 11 Cˆandido, M. M., 10, 21 Ananias Neto, J., 8 Cabella, B. C. T., 21 Andrade Jr, J. S. A., 35, 69 Cabral, R. A., 36 Andrade, H., 39 Cadilhe, A., 28, 38 Andrade, J. S., 36, 79, 82 Caldas, I. L., 15, 75 Andrade, R., 66 Caliri, A., 58 Andrade, R. F. S., 50, 75 Calv˜ao, A. M., 80 Anteneodo, C., 24, 43, 52, 62, 79, 80 Camargo, S., 24 Antunes, F. L., 7 Camelo Neto, G., 53 Aquino, R. R., 44 Campos†, P. R. A., 4 Ara´ujo, I. G., 45 Campos, J. G. F., 6 Ara´ujo, M. S., 5 Araujo, A. D., 35 Canals, S., 82 Arcisio-Miranda2, M., 31 Canet, L., 19 Arenas, Z. G., 20, 42, 77 Canova, G., 27 Arenzon, J. J., 1, 13, 27, 53, 71 Canuto, S., 27 ´ Argolo, C., 68 Caparica, A. A., 7 Assis, T. A., 42, 49 Caprio, D. D., 78 Avella, J. C. G., 82 Cardim, L., 32 Azevedo, D. L., 12 Cardoso, T. F., 38 Azevedo, S. M., 62 Carlson, B. V., 34 Carrasco, I. S. S., 69, 79 Babino, A., 82 Carvalho, J., 43 Bachelard, R., 46, 48 Carvalho, J. X., 3 Bar-Yam, Y., 52 Carvalho, R., 32 Barbosa, M. A. A., 44 Carvalho, R. S. M., 10 Barbosa, M. C., 73, 82, 83 Carvalho, S. J., 27 Barbosa, M. C. B., 82 Carvalho, T. T. A., 11 Barbosa, O. A., 67 Casas, G. A., 12 Barboza Jr, E. M. B., 8 Casetti, L., 48 Barci, D. G., 20, 42, 77 Castro, T. T. M., 67 Barros, A., 66 Caticha, N., 3, 20, 34 Batista, J. L. P., 63 Cazaubiel, A., 1 Beatrici, C., 24 Celardo, G. L., 48 Beatrici, C. P., 23 Cerdeira, H. A., 74 Beims, M. W., 15 Ch´avez, A. T., 69 Benetti, F. P. C., 7, 47 Chame, A., 68 Bernardes, A. T., 33 Chao, D., 23 85 86 Chat´e, H., 19, 57 Ferreira Junior, S. C., 22 Cherstvy, A. G., 27 Ferreira§, F. F., 4 Chimanski, E. V., 34 Ferreira, C., 35 Cintio, P. D., 48 Ferreira, D. S. R., 65 Clauset, A., 1 Ferreira, F. F., 58 Coelho, R. C. V., 71 Ferreira, R. M. S., 12 Colombo, E. H., 52 Ferreira, R. S., 37 Coniglio, A., 1 Ferreira, S. C., 10, 37, 41, 43, 66, 81 Copelli, M., 6, 54 Ferreira, S. O., 78 Corberi, F., 78 Ferreira, W. C., 74 Cordeiro, A. J. A., 65 Fid´elis, A. J., 15 Correia, R. R. B., 25 Figueirˆedo, P. H., 17, 33, 41 Cosenza, M. G., 82 Figueiredo, A., 39 Costa J´unior, F. M., 39 Figueiredo, T. P., 8 Costa, A. A., 6 Figuereido, A., 9 Costa, B. V., 8, 26, 28, 38 Filoche, M., 48 Costa, E. C., 42, 43 Fiore, C. E., 51, 73 Costa, F. H. S., 31 Fischer, R., 25 Costa, G. H. S., 41 Fonceca Junior, J. I., 17 Costa, I. V. L., 19, 38 Fontele, F. F. M., 44 Costa, M. C., 32 Forgerini, F. L., 37, 80 Costa, M. L. M., 9 Fran¸ca, G., 27 Costa, R. A., 37 Freitas, D. B., 76 Cota, W. F. C., 10 Frery, A., 24 Courteille, P. W., 46 Frey, J., 63 Coutinho, S., 53 Frigori, R. B., 39, 59 Crokidakis, N., 4, 33, 80 Fuentes-Azcatl, R., 82 Cugliandolo, L., 79 Furlan, A. P., 73 Cugliandolo, L. F., 13 Cunha, B. R., 81 Galam, S., 80 Cunha, M. V., 36 Galanti, G. R., 9 Cunha, S. D., 61 Galv˜ao, R. M. O., 70 Curado, E. M. F., 12, 75 Galv˜ao, V., 35 Gentle, K. W., 15 Dantas, W. G., 74 Gilboa, D., 25 Defaveri, L. A. E., 43 Girardi-Schappo, M., 30 Delamotte, B., 19 Giugli, E., 51 Demontiˆezo, F. L. L., 44 Gomes, M. A. F., 11, 74 DeSouza, O., 32 Gomes, M. F. C., 23 Dettmann, C. P., 75 Gomes-Gardenes, J., 66 Diaz-Mendez, R., 18 Gon¸calves, M. A. M. S., 36 Dickman, A. G., 23 Gon¸calves, S., 81 Dickman, R., 20, 23, 30, 61 Gonnella, G., 79 Diehl, A., 17 Gonsalves, J. J., 30 Doria, M. M., 71 Gonz´alez, I., 67 Dornelas, V., 62 Gonz´alez-Avella, J. C., 81 Dorogovtsev, S. N., 37 Granzotti, C. R. F., 17 Guarieiro, L. L. N., 62 Elsas, J. H. C. G., 61 Guerrero, A., 50 Erichsen J´unior, R., 58 Guimar˜aes, P. H., 13 Erichsen Jr, R., 73 Guimar˜aes-Filho, Z. O., 15 Erichsen Jr, R. E., 59 Gupta, S., 48 Escaff, D., 29 Gusso, A., 74 Essex, J., 63 Halloran, M. E., 23 F Junior, M. F., 9 Hase, M., 68 Farias, T. S., 72 Havlin, S., 79 Feliczaki, R. M., 41 Helay¨el-Neto, J. A., 5 Fernandes, H. C. M., 18 Henkel, M., 68 Ferraz, M. S. A., 61 Henriques, M. V. C., 64 Ferreira J´unior, S. C., 79 Henriques, V. B., 57 87 Herrera, J. L., 82 Machado, R. P. L., 3 Hickman, J. M., 25 Magalh˜aes, C. F. M., 36 Hirata, F. M. R., 41 Magno, W. C., 17 Hu, Y., 82 Makse, H. A., 79, 82 Huang‡, W., 4 Marinho, A. A. A., 70 Marini, S., 46, 68, 69 Idiart, M., 55 Marins, A., 32 Idiart, M. A. P., 60 Martinas, A. B., 52 Ilha, A., 71 Martinez, A. S., 17, 21 Iorra, P., 46, 69 Martins, D. C., 63 Izzo, D., 56 Martins, K. B., 11 Martins, L. C., 15 JARA, D. A. C., 67 Martins, M. L., 30 Jorge, L. N., 7 Mata, A. S., 4, 22 Julvito, W. R., 38 Mayboroda, S., 48 Maziero, J., 72 Kaiser, R., 46 Medeiros1, D., 31 Kastner, M., 48 Mello, B. A., 19 Kihara, A. H., 61 Melo, K., 37 Kinasz, M., 65 Mendes, J. F. F., 37 Kinouchi, O., 6, 9 Mendon¸ca, J. R. G., 1, 21 Klaczko, L. B., 30 Mendoza-Coto, A., 18 Kloss, T., 19 Menezes, M. A., 53 Kogan, M., 1 Metzler, R., 27 Krein, G., 40, 71 Mihara, A., 5 Kremer, G. M., 55 Miramontes, O., 31 Kroetz, T., 14, 63 Miranda, J. G. V., 62 Krott, L. B., 82, 83 Miyazima, S., 54 Kurths, J., 24 Mizusaki, B. E. P., 58, 59 Molin, J. P. D., 58 L¨utz, A. F., 1 Mondaini, A., 80 Landi, G. T., 13 Mondaini, F., 38 Lazo, M. J., 5 Moreira, A. A., 69 Leal, M. R., 59 Moreira, A. A. M., 36 Leite, F. E. A., 64 Moreira, D. M., 7 Lenin†, J., 4 Moreno, M. V., 20, 42, 77 Leonel, E. D., 75 Moret, M. A., 7, 60, 62–65, 76 Lerner, E., 51 Morgado, W. A. M., 10, 19, 21, 43 Levin, Y., 7, 27, 47, 68 Moriconi, L., 38, 49 Lima Filho, J. A., 58 Moriconi, L. R. A., 61 Lima12, A., 40 Moura, F. A. B. F., 49, 72 Lima, F. W. S., 10 Lima, J. P., 74 Nagai, M., 52 Lima, M. S., 65 Nakamura, G. M., 21 Lima, T. A., 16 Nascimento Filho, A., 62 Lindenberg, K., 29 Nascimento Filho, A. S., 62 Livorati, A. L. P., 75 Nicolao, L., 18 Longford, F., 63 Nobre, F. D., 12, 75 Longini Jr, I. L., 23 Nogueira, T. P. O., 32 Lopes, A. A., 73 Novaes, R. C., 53 Loureiro, M. P. O., 13 Nunes, R. C., 8 Louren¸co, J. A., 8 Nunes, T. C., 36 Lucena, L. S., 64 Luz, M. G. E., 46, 51 O Jr, Z. T., 8 Luzzi, R., 12, 16 Olivares, C., 43 Lyra, M. L., 48, 68 Oliveira Junior, H. A., 14, 15 Oliveira Junior, P. S. L., 65 M´aximo, C. E., 46 Oliveira Junior, S. C., 6 M´ol, L. A. S., 2, 26 Oliveira, A. C., 40 Macˆedo, A. M. S., 67 Oliveira, D. L. S., 44 Machado, B. A., 65 Oliveira, D. M., 2 88 Oliveira, D. S., 70 Rocha Filho, T. M., 11, 47 Oliveira, F. A., 12, 19, 38, 44 Rocha, A. R. L., 71 Oliveira, H. A., 15 Rocha, J. C. S., 8, 26 Oliveira, M. J., 13, 19, 56 Rocha, M. S., 30 Oliveira, M. M., 43, 51 Rocha-Filho, T. M., 8 Oliveira, P. M. C., 40, 47, 71, 79 Rodrigues Neto, C., 6 Oliveira, T. J., 69, 78, 79 Rodrigues, C. G., 12, 16 Oliveira, V. M., 58 Rosa Jr, A. C. P. R., 64 Orozco, S., 31 Rosa, R. R., 25 Ospina, R., 24 Rosembach, T. V., 30 Rossi, L., 23 Pacobahyba, J. T. M., 45 Rosso, O. A., 24 Paiva, L. R., 31 Rusch, F. R., 42 Pakter, R., 7, 46, 47, 68 Parente, W. E. F., 45 S J´unior, E. J. S., 34 Pastor-Satorras, R., 4, 57, 66 Saba, H., 62 Paula, J. O. R., 40 Sales, M. O., 49 Paulo, S. R., 25 Salinas, S., 57 Pazetti, M., 39 Salinas, S. R., 50 Peliti, L., 29 Sampaio Filho, C. I. N., 69 Pereira, F. A. C., 15 Sander, R. S., 66 Pereira, H. B. B., 36, 64, 65 Santana, M. C., 60 Pereira, R. F., 74 Santos, A. A., 30, 33 Pessoa, J. P. G., 41 Santos, A. A. B., 62 Peter, E., 69 Santos, J. V. C., 7 Peter, E. A., 46 Santos, T. B., 69 Piazza, F., 32 Sautter, R., 25 Pierre-Louis, O., 68 Sbrissia, A., 11 Pinho, E. S., 73 Schwaemmle, V., 53 Pinho, S., 32, 66 Segatto, B. R., 71 Pinto, L. T., 30 Serafim, V. L., 44 Piontti, A. P. Y., 23 Shao, J., 79 Piovella, N., 46 Sigman, M., 82 Plascak, J. A., 9 Silberberg, Y., 25 Pollito, L. G. L. F., 45 Silva, E.´ M., 72 Prado, C. P. C., 5 Silva, A. W., 11 Prado, S. D., 25 Silva, C. A. B., 12, 45 Prado, T. G., 15 Silva, D., 35 Silva, F. B. V., 44 Queir´os, S. M. D., 10, 19, 21 Silva, F. S., 60 Querino, A. L. B., 2 Silva, J. K. L., 6, 34 Silva, L. C., 41 Rˆego, H. H. A., 54 Silva, L. R., 2, 3, 14, 51 Rabelo, J. N. T., 45 Silva, L. R. S., 36 Rajesh, R., 28 Silva, M. A. A., 17, 31 Ramos, J. G., 12 Silva, P. C. A., 30 Ramos, M., 79 Silva, R. L., 14 Ramos, M. F., 80 Silva, R. P. M., 60 Ranciaro Neto, A., 72 Silva, R. R., 9 Raposo, E., 39 Silva, S. L., 14 Redner, S., 1 Silva, S. M., 35 Reis, F. D. A. A., 42, 78 Silva, S. R. M., 60 Reis, S. D. S., 79, 82 Silva, S. T., 25 Reis, S. S. E., 35 Silva, T. L. M., 68 Ribeiro, C. C., 64 Silva, T. L. M. E., 17 Ribeiro, F. L., 52 Silva, T. M., 33 Ribeiro-Teixeira, A. C., 25, 47 Silva, V. S. T., 50 Riedl, M., 24 Silva, W. M. L., 44 Riera, R., 35 Silva-Gon¸calves2, L. C., 31 Rizzato, F., 47 Silvestre, C. H., 47 Rizzato, F. B., 46, 68, 69 Sim˜oes Filho, M., 39 89 Sim˜oes, R. E. O., 1 Wyart, M., 51 Siqueira, K. M., 16 Skylaris, C., 63 Zimdahl, W., 55 Soares, A. A., 30 Solano Neto, ., 39 Sousa, G., 63 Sousa, J. R., 45 Sousa, K. R. A., 17 Souza, A. J. F., 51 Souza, A. M. C., 75 Souza, J. W. G., 62 Souza, L. F., 11 Souza, M. M., 71 Souza, P. V. S., 47 Stanley, H. E., 54 Stariolo, D., 18, 50 Steiner, J. R., 8 Stilck, J. F., 28, 69 Suma, A., 79 Susin, E. D., 58, 59 Takeuchi, K. A., 79 Tamashiro, M. N., 70 Teixeira, M. G., 32 Teles, T. N., 47, 48 Ter¸cariol, C. A. S., 21 Timpanaro, A. M., 5, 36, 80 Tinti, L., 66 Tirnakli, U., 76 Tom´e, T., 13, 19, 22, 41 Toufen, D. L., 15 Tragtenberg, M. H. R., 30, 65 Tsallis, C., 2, 29 Tucci, K., 82 Vainstein, M. H., 18, 53 Vannucchi, F. S., 5, 12 Vaveliuk, P., 64 Venancio, B. F., 46 Verg`es, M. C., 15 Vespignani, A., 23 Viana, E. R., 14 Vicentini, E., 34, 41 Vidal, I., 25 Vieira, A. P., 34 Vieira, A. R., 33 Vieira, T. M., 14, 51 Villavicencio, A., 55 Viswanathan, G. M., 14, 51 Wada, A. H. O., 13 Wanzeller, W. G., 10 Wardil, L., 34 Wardill, L., 6 Weber, G., 59, 60 Weberszpil, J., 5 Wessel, N., 24 Wilkens, R., 55 Woitek, M., 40, 71 Wood, K., 29 Wschebor, N., 19